diff --git a/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.compile.pass.cpp b/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.compile.pass.cpp
new file mode 100644
index 0000000000..1b5000f597
--- /dev/null
+++ b/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.compile.pass.cpp
@@ -0,0 +1,51 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+// SPDX-FileCopyrightText: Copyright (c) 2023 NVIDIA CORPORATION & AFFILIATES
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14
+
+// template<class I>
+//   concept permutable = see below; // Since C++20
+
+#include <cuda/std/iterator>
+
+#include "test_iterators.h"
+
+using AllConstraintsSatisfied = forward_iterator<int*>;
+static_assert( cuda::std::forward_iterator<AllConstraintsSatisfied>);
+static_assert( cuda::std::indirectly_movable_storable<AllConstraintsSatisfied, AllConstraintsSatisfied>);
+static_assert( cuda::std::indirectly_swappable<AllConstraintsSatisfied>);
+static_assert( cuda::std::permutable<AllConstraintsSatisfied>);
+
+using NotAForwardIterator = cpp20_input_iterator<int*>;
+static_assert(!cuda::std::forward_iterator<NotAForwardIterator>);
+static_assert( cuda::std::indirectly_movable_storable<NotAForwardIterator, NotAForwardIterator>);
+static_assert( cuda::std::indirectly_swappable<NotAForwardIterator>);
+static_assert(!cuda::std::permutable<NotAForwardIterator>);
+
+struct NonCopyable {
+  NonCopyable(const NonCopyable&) = delete;
+  NonCopyable& operator=(const NonCopyable&) = delete;
+  __host__ __device__ friend void swap(NonCopyable&, NonCopyable&);
+};
+using NotIMS = forward_iterator<NonCopyable*>;
+
+static_assert( cuda::std::forward_iterator<NotIMS>);
+static_assert(!cuda::std::indirectly_movable_storable<NotIMS, NotIMS>);
+static_assert( cuda::std::indirectly_swappable<NotIMS>);
+static_assert(!cuda::std::permutable<NotIMS>);
+
+// Note: it is impossible for an iterator to satisfy `indirectly_movable_storable` but not `indirectly_swappable`:
+// `indirectly_swappable` requires both iterators to be `indirectly_readable` and for `ranges::iter_swap` to be
+// well-formed for both iterators. `indirectly_movable_storable` also requires the iterator to be `indirectly_readable`.
+// `ranges::iter_swap` is always defined for `indirectly_movable_storable` iterators.
+
+int main(int, char**)
+{
+  return 0;
+}
diff --git a/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.subsumption.compile.pass.cpp b/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.subsumption.compile.pass.cpp
new file mode 100644
index 0000000000..c88508bc33
--- /dev/null
+++ b/libcudacxx/.upstream-tests/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.subsumption.compile.pass.cpp
@@ -0,0 +1,26 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+// SPDX-FileCopyrightText: Copyright (c) 2023 NVIDIA CORPORATION & AFFILIATES
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+
+// template<class I>
+//   concept permutable = see below; // Since C++20
+
+#include <cuda/std/iterator>
+
+template<class I> __host__ __device__ void test_subsumption() requires cuda::std::forward_iterator<I>;
+template<class I> __host__ __device__ void test_subsumption() requires cuda::std::indirectly_movable_storable<I, I>;
+template<class I> __host__ __device__ void test_subsumption() requires cuda::std::indirectly_swappable<I, I>;
+template<class I> __host__ __device__ constexpr bool test_subsumption() requires cuda::std::permutable<I> { return true; }
+static_assert(test_subsumption<int*>());
+
+int main(int, char**)
+{
+  return 0;
+}
diff --git a/libcudacxx/include/cuda/std/detail/libcxx/include/CMakeLists.txt b/libcudacxx/include/cuda/std/detail/libcxx/include/CMakeLists.txt
index 0593b4909b..74d3a74c7d 100644
--- a/libcudacxx/include/cuda/std/detail/libcxx/include/CMakeLists.txt
+++ b/libcudacxx/include/cuda/std/detail/libcxx/include/CMakeLists.txt
@@ -102,6 +102,7 @@ set(files
   __iterator/next.h
   __iterator/ostream_iterator.h
   __iterator/ostreambuf_iterator.h
+  __iterator/permutable.h
   __iterator/prev.h
   __iterator/readable_traits.h
   __iterator/reverse_access.h
diff --git a/libcudacxx/include/cuda/std/detail/libcxx/include/__iterator/permutable.h b/libcudacxx/include/cuda/std/detail/libcxx/include/__iterator/permutable.h
new file mode 100644
index 0000000000..2c751c6d0e
--- /dev/null
+++ b/libcudacxx/include/cuda/std/detail/libcxx/include/__iterator/permutable.h
@@ -0,0 +1,53 @@
+// -*- C++ -*-
+//===----------------------------------------------------------------------===//
+//
+// 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
+// SPDX-FileCopyrightText: Copyright (c) 2023 NVIDIA CORPORATION & AFFILIATES
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCUDACXX___ITERATOR_PERMUTABLE_H
+#define _LIBCUDACXX___ITERATOR_PERMUTABLE_H
+
+#ifndef __cuda_std__
+#include <__config>
+#endif // __cuda_std__
+
+#include "../__iterator/concepts.h"
+#include "../__iterator/iter_swap.h"
+
+#if defined(_LIBCUDACXX_USE_PRAGMA_GCC_SYSTEM_HEADER)
+#pragma GCC system_header
+#endif
+
+_LIBCUDACXX_BEGIN_NAMESPACE_STD
+
+#if _LIBCUDACXX_STD_VER > 17
+
+template <class _Iterator>
+concept permutable =
+    forward_iterator<_Iterator> &&
+    indirectly_movable_storable<_Iterator, _Iterator> &&
+    indirectly_swappable<_Iterator, _Iterator>;
+
+#elif _LIBCUDACXX_STD_VER > 14
+
+template<class _Iterator>
+_LIBCUDACXX_CONCEPT_FRAGMENT(
+  __permutable_,
+  requires()(
+    requires(forward_iterator<_Iterator>),
+    requires(indirectly_movable_storable<_Iterator, _Iterator>),
+    requires(indirectly_swappable<_Iterator, _Iterator>)
+  ));
+
+template <class _Iterator>
+_LIBCUDACXX_CONCEPT permutable = _LIBCUDACXX_FRAGMENT(__permutable_, _Iterator);
+
+#endif // _LIBCUDACXX_STD_VER > 14
+
+_LIBCUDACXX_END_NAMESPACE_STD
+
+#endif // _LIBCUDACXX___ITERATOR_PERMUTABLE_H
diff --git a/libcudacxx/include/cuda/std/detail/libcxx/include/iterator b/libcudacxx/include/cuda/std/detail/libcxx/include/iterator
index 45830625dd..3e797f900d 100644
--- a/libcudacxx/include/cuda/std/detail/libcxx/include/iterator
+++ b/libcudacxx/include/cuda/std/detail/libcxx/include/iterator
@@ -702,6 +702,7 @@ template <class E> constexpr const E* data(initializer_list<E> il) noexcept;
 #include "__iterator/next.h"
 #include "__iterator/ostream_iterator.h"
 #include "__iterator/ostreambuf_iterator.h"
+#include "__iterator/permutable.h"
 #include "__iterator/prev.h"
 #include "__iterator/readable_traits.h"
 #include "__iterator/reverse_access.h"
diff --git a/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.compile.pass.cpp b/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.compile.pass.cpp
new file mode 100644
index 0000000000..54d5d46450
--- /dev/null
+++ b/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.compile.pass.cpp
@@ -0,0 +1,49 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+
+// template<class I>
+//   concept permutable = see below; // Since C++20
+
+#include <iterator>
+
+#include "test_iterators.h"
+
+using AllConstraintsSatisfied = forward_iterator<int*>;
+static_assert( std::forward_iterator<AllConstraintsSatisfied>);
+static_assert( std::indirectly_movable_storable<AllConstraintsSatisfied, AllConstraintsSatisfied>);
+static_assert( std::indirectly_swappable<AllConstraintsSatisfied>);
+static_assert( std::permutable<AllConstraintsSatisfied>);
+
+using NotAForwardIterator = cpp20_input_iterator<int*>;
+static_assert(!std::forward_iterator<NotAForwardIterator>);
+static_assert( std::indirectly_movable_storable<NotAForwardIterator, NotAForwardIterator>);
+static_assert( std::indirectly_swappable<NotAForwardIterator>);
+static_assert(!std::permutable<NotAForwardIterator>);
+
+struct NonCopyable {
+  NonCopyable(const NonCopyable&) = delete;
+  NonCopyable& operator=(const NonCopyable&) = delete;
+  friend void swap(NonCopyable&, NonCopyable&);
+};
+using NotIMS = forward_iterator<NonCopyable*>;
+
+static_assert( std::forward_iterator<NotIMS>);
+static_assert(!std::indirectly_movable_storable<NotIMS, NotIMS>);
+static_assert( std::indirectly_swappable<NotIMS>);
+static_assert(!std::permutable<NotIMS>);
+
+// Note: it is impossible for an iterator to satisfy `indirectly_movable_storable` but not `indirectly_swappable`:
+// `indirectly_swappable` requires both iterators to be `indirectly_readable` and for `ranges::iter_swap` to be
+// well-formed for both iterators. `indirectly_movable_storable` also requires the iterator to be `indirectly_readable`.
+// `ranges::iter_swap` is always defined for `indirectly_movable_storable` iterators.
+
+int main(int, char**) {
+  return 0;
+}
diff --git a/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.subsumption.compile.pass.cpp b/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.subsumption.compile.pass.cpp
new file mode 100644
index 0000000000..9cd7f37f09
--- /dev/null
+++ b/libcudacxx/libcxx/test/std/iterators/iterator.requirements/alg.req.permutable/permutable.subsumption.compile.pass.cpp
@@ -0,0 +1,24 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+
+// template<class I>
+//   concept permutable = see below; // Since C++20
+
+#include <iterator>
+
+template<class I> void test_subsumption() requires std::forward_iterator<I>;
+template<class I> void test_subsumption() requires std::indirectly_movable_storable<I, I>;
+template<class I> void test_subsumption() requires std::indirectly_swappable<I, I>;
+template<class I> constexpr bool test_subsumption() requires std::permutable<I> { return true; }
+static_assert(test_subsumption<int*>());
+
+int main(int, char**) {
+  return 0;
+}