diff --git a/libcxx/benchmarks/CMakeLists.txt b/libcxx/benchmarks/CMakeLists.txt
--- a/libcxx/benchmarks/CMakeLists.txt
+++ b/libcxx/benchmarks/CMakeLists.txt
@@ -167,6 +167,7 @@
     algorithms/pop_heap.bench.cpp
     algorithms/push_heap.bench.cpp
     algorithms/ranges_sort.bench.cpp
+    algorithms/ranges_stable_sort.bench.cpp
     algorithms/sort.bench.cpp
     algorithms/sort_heap.bench.cpp
     algorithms/stable_sort.bench.cpp
diff --git a/libcxx/benchmarks/algorithms/ranges_stable_sort.bench.cpp b/libcxx/benchmarks/algorithms/ranges_stable_sort.bench.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/benchmarks/algorithms/ranges_stable_sort.bench.cpp
@@ -0,0 +1,39 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include <algorithm>
+
+#include "common.h"
+
+namespace {
+template <class ValueType, class Order>
+struct StableSort {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(
+        state, Quantity, Order(), BatchSize::CountElements,
+        [](auto& Copy) { std::ranges::stable_sort(Copy); });
+  }
+
+  bool skip() const { return Order() == ::Order::Heap; }
+
+  std::string name() const {
+    return "BM_RangesStableSort" + ValueType::name() + Order::name() + "_" +
+           std::to_string(Quantity);
+  }
+};
+} // namespace
+
+int main(int argc, char** argv) {
+  benchmark::Initialize(&argc, argv);
+  if (benchmark::ReportUnrecognizedArguments(argc, argv))
+    return 1;
+  makeCartesianProductBenchmark<StableSort, AllValueTypes, AllOrders>(Quantities);
+  benchmark::RunSpecifiedBenchmarks();
+}
diff --git a/libcxx/docs/Status/RangesAlgorithms.csv b/libcxx/docs/Status/RangesAlgorithms.csv
--- a/libcxx/docs/Status/RangesAlgorithms.csv
+++ b/libcxx/docs/Status/RangesAlgorithms.csv
@@ -74,7 +74,7 @@
 Permutation,partition,Not assigned,n/a,Not started
 Permutation,stable_partition,Not assigned,n/a,Not started
 Permutation,sort,Konstantin Varlamov,`D127557 <https://llvm.org/D127557>`_,✅
-Permutation,stable_sort,Konstantin Varlamov,n/a,In progress
+Permutation,stable_sort,Konstantin Varlamov,`D127834 <https://llvm.org/D127834>`_,✅
 Permutation,partial_sort,Konstantin Varlamov,n/a,In progress
 Permutation,nth_element,Not assigned,n/a,Not started
 Permutation,inplace_merge,Not assigned,n/a,Not started
diff --git a/libcxx/include/CMakeLists.txt b/libcxx/include/CMakeLists.txt
--- a/libcxx/include/CMakeLists.txt
+++ b/libcxx/include/CMakeLists.txt
@@ -106,6 +106,7 @@
   __algorithm/ranges_replace_if.h
   __algorithm/ranges_reverse.h
   __algorithm/ranges_sort.h
+  __algorithm/ranges_stable_sort.h
   __algorithm/ranges_swap_ranges.h
   __algorithm/ranges_transform.h
   __algorithm/ranges_upper_bound.h
diff --git a/libcxx/include/__algorithm/ranges_sort.h b/libcxx/include/__algorithm/ranges_sort.h
--- a/libcxx/include/__algorithm/ranges_sort.h
+++ b/libcxx/include/__algorithm/ranges_sort.h
@@ -11,7 +11,6 @@
 
 #include <__algorithm/make_projected.h>
 #include <__algorithm/sort.h>
-#include <__concepts/same_as.h>
 #include <__config>
 #include <__functional/identity.h>
 #include <__functional/invoke.h>
@@ -44,7 +43,7 @@
   _Iter __sort_fn_impl(_Iter __first, _Sent __last, _Comp& __comp, _Proj& __proj) {
     auto __last_iter = ranges::next(__first, __last);
 
-    auto&& __projected_comp = __make_projected_comp(__comp, __proj);
+    auto&& __projected_comp = ranges::__make_projected_comp(__comp, __proj);
     std::__sort_impl(std::move(__first), __last_iter, __projected_comp);
 
     return __last_iter;
diff --git a/libcxx/include/__algorithm/ranges_sort.h b/libcxx/include/__algorithm/ranges_stable_sort.h
copy from libcxx/include/__algorithm/ranges_sort.h
copy to libcxx/include/__algorithm/ranges_stable_sort.h
--- a/libcxx/include/__algorithm/ranges_sort.h
+++ b/libcxx/include/__algorithm/ranges_stable_sort.h
@@ -6,12 +6,11 @@
 //
 //===----------------------------------------------------------------------===//
 
-#ifndef _LIBCPP___ALGORITHM_RANGES_SORT_H
-#define _LIBCPP___ALGORITHM_RANGES_SORT_H
+#ifndef _LIBCPP___ALGORITHM_RANGES_STABLE_SORT_H
+#define _LIBCPP___ALGORITHM_RANGES_STABLE_SORT_H
 
 #include <__algorithm/make_projected.h>
-#include <__algorithm/sort.h>
-#include <__concepts/same_as.h>
+#include <__algorithm/stable_sort.h>
 #include <__config>
 #include <__functional/identity.h>
 #include <__functional/invoke.h>
@@ -36,39 +35,39 @@
 _LIBCPP_BEGIN_NAMESPACE_STD
 
 namespace ranges {
-namespace __sort {
+namespace __stable_sort {
 
 struct __fn {
   template <class _Iter, class _Sent, class _Comp, class _Proj>
-  _LIBCPP_HIDE_FROM_ABI constexpr static
-  _Iter __sort_fn_impl(_Iter __first, _Sent __last, _Comp& __comp, _Proj& __proj) {
+  _LIBCPP_HIDE_FROM_ABI
+  static _Iter __stable_sort_fn_impl(_Iter __first, _Sent __last, _Comp& __comp, _Proj& __proj) {
     auto __last_iter = ranges::next(__first, __last);
 
-    auto&& __projected_comp = __make_projected_comp(__comp, __proj);
-    std::__sort_impl(std::move(__first), __last_iter, __projected_comp);
+    auto&& __projected_comp = ranges::__make_projected_comp(__comp, __proj);
+    std::__stable_sort_impl(std::move(__first), __last_iter, __projected_comp);
 
     return __last_iter;
   }
 
   template <random_access_iterator _Iter, sentinel_for<_Iter> _Sent, class _Comp = ranges::less, class _Proj = identity>
     requires sortable<_Iter, _Comp, _Proj>
-  _LIBCPP_HIDE_FROM_ABI constexpr
+  _LIBCPP_HIDE_FROM_ABI
   _Iter operator()(_Iter __first, _Sent __last, _Comp __comp = {}, _Proj __proj = {}) const {
-    return __sort_fn_impl(std::move(__first), std::move(__last), __comp, __proj);
+    return __stable_sort_fn_impl(std::move(__first), std::move(__last), __comp, __proj);
   }
 
   template <random_access_range _Range, class _Comp = ranges::less, class _Proj = identity>
     requires sortable<iterator_t<_Range>, _Comp, _Proj>
-  _LIBCPP_HIDE_FROM_ABI constexpr
+  _LIBCPP_HIDE_FROM_ABI
   borrowed_iterator_t<_Range> operator()(_Range&& __r, _Comp __comp = {}, _Proj __proj = {}) const {
-    return __sort_fn_impl(ranges::begin(__r), ranges::end(__r), __comp, __proj);
+    return __stable_sort_fn_impl(ranges::begin(__r), ranges::end(__r), __comp, __proj);
   }
 };
 
-} // namespace __sort
+} // namespace __stable_sort
 
 inline namespace __cpo {
-  inline constexpr auto sort = __sort::__fn{};
+  inline constexpr auto stable_sort = __stable_sort::__fn{};
 } // namespace __cpo
 } // namespace ranges
 
@@ -76,4 +75,4 @@
 
 #endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
 
-#endif // _LIBCPP___ALGORITHM_RANGES_SORT_H
+#endif // _LIBCPP___ALGORITHM_RANGES_STABLE_SORT_H
diff --git a/libcxx/include/__algorithm/stable_sort.h b/libcxx/include/__algorithm/stable_sort.h
--- a/libcxx/include/__algorithm/stable_sort.h
+++ b/libcxx/include/__algorithm/stable_sort.h
@@ -15,6 +15,7 @@
 #include <__algorithm/sort.h>
 #include <__config>
 #include <__iterator/iterator_traits.h>
+#include <__utility/move.h>
 #include <__utility/swap.h>
 #include <memory>
 #include <type_traits>
@@ -199,33 +200,36 @@
 }
 
 template <class _RandomAccessIterator, class _Compare>
-inline _LIBCPP_INLINE_VISIBILITY
-void
-stable_sort(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp)
-{
-    typedef typename iterator_traits<_RandomAccessIterator>::value_type value_type;
-    typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
-    difference_type __len = __last - __first;
-    pair<value_type*, ptrdiff_t> __buf(0, 0);
-    unique_ptr<value_type, __return_temporary_buffer> __h;
-    if (__len > static_cast<difference_type>(__stable_sort_switch<value_type>::value))
-    {
+inline _LIBCPP_HIDE_FROM_ABI
+void __stable_sort_impl(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare& __comp) {
+  using value_type = typename iterator_traits<_RandomAccessIterator>::value_type;
+  using difference_type = typename iterator_traits<_RandomAccessIterator>::difference_type;
+
+  difference_type __len = __last - __first;
+  pair<value_type*, ptrdiff_t> __buf(0, 0);
+  unique_ptr<value_type, __return_temporary_buffer> __h;
+  if (__len > static_cast<difference_type>(__stable_sort_switch<value_type>::value)) {
 // TODO: Remove the use of std::get_temporary_buffer
 _LIBCPP_SUPPRESS_DEPRECATED_PUSH
-        __buf = _VSTD::get_temporary_buffer<value_type>(__len);
+      __buf = std::get_temporary_buffer<value_type>(__len);
 _LIBCPP_SUPPRESS_DEPRECATED_POP
-        __h.reset(__buf.first);
-    }
-    typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
-    _VSTD::__stable_sort<_Comp_ref>(__first, __last, __comp, __len, __buf.first, __buf.second);
+      __h.reset(__buf.first);
+  }
+
+  using _Comp_ref = typename __comp_ref_type<_Compare>::type;
+  std::__stable_sort<_Comp_ref>(__first, __last, __comp, __len, __buf.first, __buf.second);
+}
+
+template <class _RandomAccessIterator, class _Compare>
+inline _LIBCPP_HIDE_FROM_ABI
+void stable_sort(_RandomAccessIterator __first, _RandomAccessIterator __last, _Compare __comp) {
+  std::__stable_sort_impl(std::move(__first), std::move(__last), __comp);
 }
 
 template <class _RandomAccessIterator>
-inline _LIBCPP_INLINE_VISIBILITY
-void
-stable_sort(_RandomAccessIterator __first, _RandomAccessIterator __last)
-{
-    _VSTD::stable_sort(__first, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
+inline _LIBCPP_HIDE_FROM_ABI
+void stable_sort(_RandomAccessIterator __first, _RandomAccessIterator __last) {
+  std::stable_sort(__first, __last, __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
 }
 
 _LIBCPP_END_NAMESPACE_STD
diff --git a/libcxx/include/algorithm b/libcxx/include/algorithm
--- a/libcxx/include/algorithm
+++ b/libcxx/include/algorithm
@@ -287,7 +287,6 @@
            indirect_unary_predicate<projected<iterator_t<R>, Proj>> Pred>
     constexpr bool ranges::is_partitioned(R&& r, Pred pred, Proj proj = {});                // since C++20
 
-
   template<bidirectional_iterator I, sentinel_for<I> S>
     requires permutable<I>
     constexpr I ranges::reverse(I first, S last);                                           // since C++20
@@ -300,12 +299,22 @@
             class Proj = identity>
     requires sortable<I, Comp, Proj>
     constexpr I
-      sort(I first, S last, Comp comp = {}, Proj proj = {});                                // since C++20
+      ranges::sort(I first, S last, Comp comp = {}, Proj proj = {});                        // since C++20
 
   template<random_access_range R, class Comp = ranges::less, class Proj = identity>
     requires sortable<iterator_t<R>, Comp, Proj>
     constexpr borrowed_iterator_t<R>
-      sort(R&& r, Comp comp = {}, Proj proj = {});                                          // since C++20
+      ranges::sort(R&& r, Comp comp = {}, Proj proj = {});                                  // since C++20
+
+  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+          class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    I ranges::stable_sort(I first, S last, Comp comp = {}, Proj proj = {});                 // since C++20
+
+  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    borrowed_iterator_t<R>
+      ranges::stable_sort(R&& r, Comp comp = {}, Proj proj = {});                           // since C++20
 
   template<class T, output_iterator<const T&> O, sentinel_for<O> S>
     constexpr O ranges::fill(O first, S last, const T& value);                              // since C++20
@@ -1252,6 +1261,7 @@
 #include <__algorithm/ranges_replace_if.h>
 #include <__algorithm/ranges_reverse.h>
 #include <__algorithm/ranges_sort.h>
+#include <__algorithm/ranges_stable_sort.h>
 #include <__algorithm/ranges_swap_ranges.h>
 #include <__algorithm/ranges_transform.h>
 #include <__algorithm/ranges_upper_bound.h>
diff --git a/libcxx/include/module.modulemap.in b/libcxx/include/module.modulemap.in
--- a/libcxx/include/module.modulemap.in
+++ b/libcxx/include/module.modulemap.in
@@ -345,6 +345,7 @@
       module ranges_replace_if               { private header "__algorithm/ranges_replace_if.h" }
       module ranges_reverse                  { private header "__algorithm/ranges_reverse.h" }
       module ranges_sort                     { private header "__algorithm/ranges_sort.h" }
+      module ranges_stable_sort              { private header "__algorithm/ranges_stable_sort.h" }
       module ranges_swap_ranges              { private header "__algorithm/ranges_swap_ranges.h" }
       module ranges_transform                { private header "__algorithm/ranges_transform.h" }
       module ranges_upper_bound              { private header "__algorithm/ranges_upper_bound.h" }
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
@@ -213,8 +213,8 @@
     //(void)std::ranges::sort_heap(a, Less(&copies)); assert(copies == 0);
     //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_partition(first, last, UnaryTrue(&copies)); assert(copies == 0); }
     //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_partition(a, UnaryTrue(&copies)); assert(copies == 0); }
-    //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(first, last, Less(&copies)); assert(copies == 0); }
-    //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(a, Less(&copies)); assert(copies == 0); }
+    if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(first, last, Less(&copies)); assert(copies == 0); }
+    if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(a, Less(&copies)); assert(copies == 0); }
 #if TEST_STD_VER > 20
     //(void)std::ranges::starts_with(first, last, first2, last2, Equal(&copies)); assert(copies == 0);
 #endif
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
@@ -204,8 +204,8 @@
     //(void)std::ranges::sort_heap(a, Less(), Proj(&copies)); assert(copies == 0);
     //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_partition(first, last, UnaryTrue(), Proj(&copies)); assert(copies == 0); }
     //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_partition(a, UnaryTrue(), Proj(&copies)); assert(copies == 0); }
-    //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(first, last, Less(), Proj(&copies)); assert(copies == 0); }
-    //if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(a, Less(), Proj(&copies)); assert(copies == 0); }
+    if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(first, last, Less(), Proj(&copies)); assert(copies == 0); }
+    if (!std::is_constant_evaluated()) { (void)std::ranges::stable_sort(a, Less(), Proj(&copies)); assert(copies == 0); }
 #if TEST_STD_VER > 20
     //(void)std::ranges::starts_with(first, last, first2, last2, Equal(), Proj(&copies), Proj(&copies)); assert(copies == 0);
 #endif
diff --git a/libcxx/test/libcxx/private_headers.verify.cpp b/libcxx/test/libcxx/private_headers.verify.cpp
--- a/libcxx/test/libcxx/private_headers.verify.cpp
+++ b/libcxx/test/libcxx/private_headers.verify.cpp
@@ -143,6 +143,7 @@
 #include <__algorithm/ranges_replace_if.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_replace_if.h'}}
 #include <__algorithm/ranges_reverse.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_reverse.h'}}
 #include <__algorithm/ranges_sort.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_sort.h'}}
+#include <__algorithm/ranges_stable_sort.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_stable_sort.h'}}
 #include <__algorithm/ranges_swap_ranges.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_swap_ranges.h'}}
 #include <__algorithm/ranges_transform.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_transform.h'}}
 #include <__algorithm/ranges_upper_bound.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_upper_bound.h'}}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.sort/stable.sort/ranges.stable.sort.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.sort/stable.sort/ranges.stable.sort.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.sort/stable.sort/ranges.stable.sort.pass.cpp
@@ -0,0 +1,269 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// <algorithm>
+
+// template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+//         class Proj = identity>
+//   requires sortable<I, Comp, Proj>
+//   I ranges::stable_sort(I first, S last, Comp comp = {}, Proj proj = {});                 // since C++20
+//
+// template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+//   requires sortable<iterator_t<R>, Comp, Proj>
+//   borrowed_iterator_t<R>
+//     ranges::stable_sort(R&& r, Comp comp = {}, Proj proj = {});                           // since C++20
+
+#include <algorithm>
+#include <array>
+#include <concepts>
+#include <functional>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "boolean_testable.h"
+#include "test_iterators.h"
+
+// SFINAE tests.
+
+using BadComparator = ComparatorNotCopyable<int*>;
+static_assert(!std::sortable<int*, BadComparator>);
+
+template <class Iter, class Sent = sentinel_wrapper<Iter>, class Comp = std::ranges::less>
+concept HasStableSortIt = requires(Iter first, Sent last, Comp comp) { std::ranges::stable_sort(first, last, comp); };
+
+static_assert(HasStableSortIt<int*>);
+static_assert(!HasStableSortIt<RandomAccessIteratorNotDerivedFrom>);
+static_assert(!HasStableSortIt<RandomAccessIteratorBadIndex>);
+static_assert(!HasStableSortIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasStableSortIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasStableSortIt<int*, int*, BadComparator>);
+static_assert(!HasStableSortIt<const int*>); // Doesn't satisfy `sortable`.
+
+template <class Range, class Comp = std::ranges::less>
+concept HasStableSortR = requires(Range range, Comp comp) { std::ranges::stable_sort(range, comp); };
+
+static_assert(HasStableSortR<UncheckedRange<int*>>);
+static_assert(!HasStableSortR<RandomAccessRangeNotDerivedFrom>);
+static_assert(!HasStableSortR<RandomAccessRangeBadIndex>);
+static_assert(!HasStableSortR<UncheckedRange<int*, SentinelForNotSemiregular>>);
+static_assert(!HasStableSortR<UncheckedRange<int*, SentinelForNotWeaklyEqualityComparableWith>>);
+static_assert(!HasStableSortR<UncheckedRange<int*>, BadComparator>);
+static_assert(!HasStableSortR<UncheckedRange<const int*>>); // Doesn't satisfy `sortable`.
+
+template <class Iter, class Sent, size_t N>
+void test_one(std::array<int, N> input, std::array<int, N> expected) {
+  { // (iterator, sentinel) overload.
+    auto sorted = input;
+    auto b = Iter(sorted.data());
+    auto e = Sent(Iter(sorted.data() + sorted.size()));
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::stable_sort(b, e);
+    assert(sorted == expected);
+    assert(base(last) == sorted.data() + sorted.size());
+  }
+
+  { // (range) overload.
+    auto sorted = input;
+    auto b = Iter(sorted.data());
+    auto e = Sent(Iter(sorted.data() + sorted.size()));
+    auto range = std::ranges::subrange(b, e);
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::stable_sort(range);
+    assert(sorted == expected);
+    assert(base(last) == sorted.data() + sorted.size());
+  }
+}
+
+template <class Iter, class Sent>
+void test_iterators_2() {
+  // Empty sequence.
+  test_one<Iter, Sent, 0>({}, {});
+  // 1-element sequence.
+  test_one<Iter, Sent, 1>({1}, {1});
+  // 2-element sequence.
+  test_one<Iter, Sent, 2>({2, 1}, {1, 2});
+  // 3-element sequence.
+  test_one<Iter, Sent, 3>({2, 1, 3}, {1, 2, 3});
+  // Longer sequence.
+  test_one<Iter, Sent, 8>({2, 1, 3, 6, 8, 4, 11, 5}, {1, 2, 3, 4, 5, 6, 8, 11});
+  // Longer sequence with duplicates.
+  test_one<Iter, Sent, 7>({2, 1, 3, 6, 2, 8, 6}, {1, 2, 2, 3, 6, 6, 8});
+  // All elements are the same.
+  test_one<Iter, Sent, 3>({1, 1, 1}, {1, 1, 1});
+  // Already sorted.
+  test_one<Iter, Sent, 5>({1, 2, 3, 4, 5}, {1, 2, 3, 4, 5});
+  // Reverse-sorted.
+  test_one<Iter, Sent, 5>({5, 4, 3, 2, 1}, {1, 2, 3, 4, 5});
+  // Repeating pattern.
+  test_one<Iter, Sent, 6>({1, 2, 1, 2, 1, 2}, {1, 1, 1, 2, 2, 2});
+}
+
+template <class Iter>
+void test_iterators_1() {
+  test_iterators_2<Iter, Iter>();
+  test_iterators_2<Iter, sentinel_wrapper<Iter>>();
+}
+
+void test_iterators() {
+  test_iterators_1<random_access_iterator<int*>>();
+  test_iterators_1<contiguous_iterator<int*>>();
+  test_iterators_1<int*>();
+}
+
+void test() {
+  test_iterators();
+
+  struct OrderedValue {
+    int value;
+    double original_order;
+    bool operator==(const OrderedValue&) const = default;
+    auto operator<=>(const OrderedValue& rhs) const { return value <=> rhs.value; }
+  };
+
+  { // The sort is stable (equivalent elements remain in the same order).
+    using V = OrderedValue;
+    using Array = std::array<V, 20>;
+    Array orig_in = {
+      V{10, 10.1}, {12, 12.1}, {3, 3.1}, {5, 5.1}, {3, 3.2}, {3, 3.3}, {11, 11.1}, {12, 12.2}, {4, 4.1}, {4, 4.2},
+      {4, 4.3}, {1, 1.1}, {6, 6.1}, {3, 3.4}, {10, 10.2}, {8, 8.1}, {12, 12.3}, {1, 1.2}, {1, 1.3}, {5, 5.2}
+    };
+    Array expected = {
+      V{1, 1.1}, {1, 1.2}, {1, 1.3},
+      {3, 3.1}, {3, 3.2}, {3, 3.3}, {3, 3.4},
+      {4, 4.1}, {4, 4.2}, {4, 4.3},
+      {5, 5.1}, {5, 5.2},
+      {6, 6.1},
+      {8, 8.1},
+      {10, 10.1}, {10, 10.2},
+      {11, 11.1},
+      {12, 12.1}, {12, 12.2}, {12, 12.3}
+    };
+
+    {
+      auto in = orig_in;
+      auto last = std::ranges::stable_sort(in.begin(), in.end());
+      assert(in == expected);
+      assert(last == in.end());
+    }
+
+    {
+      auto in = orig_in;
+      auto last = std::ranges::stable_sort(in);
+      assert(in == expected);
+      assert(last == in.end());
+    }
+  }
+
+  { // A custom comparator works and is stable.
+    using V = OrderedValue;
+    using Array = std::array<V, 11>;
+
+    Array orig_in = {
+      V{1, 1.1}, {2, 2.1}, {2, 2.2}, {3, 3.1}, {2, 2.3}, {3, 3.2}, {4, 4.1}, {5, 5.1}, {2, 2.4}, {5, 5.2}, {1, 1.2}
+    };
+    Array expected = {
+      V{5, 5.1}, {5, 5.2},
+      {4, 4.1},
+      {3, 3.1}, {3, 3.2},
+      {2, 2.1}, {2, 2.2}, {2, 2.3}, {2, 2.4},
+      {1, 1.1}, {1, 1.2}
+    };
+
+    {
+      auto in = orig_in;
+      auto last = std::ranges::stable_sort(in.begin(), in.end(), std::greater{});
+      assert(in == expected);
+      assert(last == in.end());
+    }
+
+    {
+      auto in = orig_in;
+      auto last = std::ranges::stable_sort(in, std::greater{});
+      assert(in == expected);
+      assert(last == in.end());
+    }
+  }
+
+  { // A custom projection works.
+    struct A {
+      int a;
+      bool operator==(const A&) const = default;
+    };
+
+    {
+      std::array in = {A{2}, A{3}, A{1}};
+      auto last = std::ranges::stable_sort(in.begin(), in.end(), {}, &A::a);
+      assert((in == std::array{A{1}, A{2}, A{3}}));
+      assert(last == in.end());
+    }
+
+    {
+      std::array in = {A{2}, A{3}, A{1}};
+      auto last = std::ranges::stable_sort(in, {}, &A::a);
+      assert((in == std::array{A{1}, A{2}, A{3}}));
+      assert(last == in.end());
+    }
+  }
+
+  { // `std::invoke` is used in the implementation.
+    struct S {
+      int i;
+      S(int i_) : i(i_) {}
+
+      bool comparator(const S& rhs) const { return i < rhs.i; }
+      const S& projection() const { return *this; }
+
+      bool operator==(const S&) const = default;
+    };
+
+    {
+      std::array in = {S{2}, S{3}, S{1}};
+      auto last = std::ranges::stable_sort(in.begin(), in.end(), &S::comparator, &S::projection);
+      assert((in == std::array{S{1}, S{2}, S{3}}));
+      assert(last == in.end());
+    }
+
+    {
+      std::array in = {S{2}, S{3}, S{1}};
+      auto last = std::ranges::stable_sort(in, &S::comparator, &S::projection);
+      assert((in == std::array{S{1}, S{2}, S{3}}));
+      assert(last == in.end());
+    }
+  }
+
+  { // The comparator can return any type that's convertible to `bool`.
+    {
+      std::array in = {2, 1, 3};
+      auto last = std::ranges::stable_sort(in.begin(), in.end(), [](int i, int j) { return BooleanTestable{i < j}; });
+      assert((in == std::array{1, 2, 3}));
+      assert(last == in.end());
+    }
+
+    {
+      std::array in = {2, 1, 3};
+      auto last = std::ranges::stable_sort(in, [](int i, int j) { return BooleanTestable{i < j}; });
+      assert((in == std::array{1, 2, 3}));
+      assert(last == in.end());
+    }
+  }
+
+  { // `std::ranges::dangling` is returned.
+    [[maybe_unused]] std::same_as<std::ranges::dangling> decltype(auto) result =
+        std::ranges::stable_sort(std::array{1, 2, 3});
+  }
+}
+
+int main(int, char**) {
+  test();
+  // Note: `stable_sort` is not `constexpr`.
+
+  return 0;
+}
diff --git a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
--- a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
+++ b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
@@ -140,7 +140,7 @@
 static_assert(test(std::ranges::sort, a));
 //static_assert(test(std::ranges::sort_heap, a));
 //static_assert(test(std::ranges::stable_partition, a, odd));
-//static_assert(test(std::ranges::stable_sort, a));
+static_assert(test(std::ranges::stable_sort, a));
 //static_assert(test(std::ranges::starts_with, a, a));
 static_assert(test(std::ranges::swap_ranges, a, a));
 static_assert(test(std::ranges::transform, a, a, triple));