diff --git a/libcxx/include/map b/libcxx/include/map
--- a/libcxx/include/map
+++ b/libcxx/include/map
@@ -907,7 +907,6 @@
     typedef value_type&                              reference;
     typedef const value_type&                        const_reference;
 
-    static_assert(sizeof(__diagnose_non_const_comparator<_Key, _Compare>()), "");
     static_assert((is_same<typename allocator_type::value_type, value_type>::value),
                   "Allocator::value_type must be same type as value_type");
 
@@ -1085,6 +1084,11 @@
             insert(__m.begin(), __m.end());
         }
 
+    _LIBCPP_INLINE_VISIBILITY
+    ~map() {
+        static_assert(sizeof(__diagnose_non_const_comparator<_Key, _Compare>()), "");
+    }
+
     _LIBCPP_INLINE_VISIBILITY
           iterator begin() _NOEXCEPT {return __tree_.begin();}
     _LIBCPP_INLINE_VISIBILITY
@@ -1638,7 +1642,6 @@
     typedef value_type&                              reference;
     typedef const value_type&                        const_reference;
 
-    static_assert(sizeof(__diagnose_non_const_comparator<_Key, _Compare>()), "");
     static_assert((is_same<typename allocator_type::value_type, value_type>::value),
                   "Allocator::value_type must be same type as value_type");
 
@@ -1817,6 +1820,11 @@
             insert(__m.begin(), __m.end());
         }
 
+    _LIBCPP_INLINE_VISIBILITY
+    ~multimap() {
+        static_assert(sizeof(__diagnose_non_const_comparator<_Key, _Compare>()), "");
+    }
+
     _LIBCPP_INLINE_VISIBILITY
           iterator begin() _NOEXCEPT {return __tree_.begin();}
     _LIBCPP_INLINE_VISIBILITY
diff --git a/libcxx/include/set b/libcxx/include/set
--- a/libcxx/include/set
+++ b/libcxx/include/set
@@ -450,7 +450,6 @@
     typedef value_type&                              reference;
     typedef const value_type&                        const_reference;
 
-    static_assert(sizeof(__diagnose_non_const_comparator<_Key, _Compare>()), "");
     static_assert((is_same<typename allocator_type::value_type, value_type>::value),
                   "Allocator::value_type must be same type as value_type");
 
@@ -596,6 +595,11 @@
         }
 #endif  // _LIBCPP_CXX03_LANG
 
+    _LIBCPP_INLINE_VISIBILITY
+    ~set() {
+        static_assert(sizeof(__diagnose_non_const_comparator<_Key, _Compare>()), "");
+    }
+
     _LIBCPP_INLINE_VISIBILITY
           iterator begin() _NOEXCEPT       {return __tree_.begin();}
     _LIBCPP_INLINE_VISIBILITY
@@ -938,7 +942,6 @@
     typedef value_type&                              reference;
     typedef const value_type&                        const_reference;
 
-    static_assert(sizeof(__diagnose_non_const_comparator<_Key, _Compare>()), "");
     static_assert((is_same<typename allocator_type::value_type, value_type>::value),
                   "Allocator::value_type must be same type as value_type");
 
@@ -1083,6 +1086,11 @@
         }
 #endif  // _LIBCPP_CXX03_LANG
 
+    _LIBCPP_INLINE_VISIBILITY
+    ~multiset() {
+        static_assert(sizeof(__diagnose_non_const_comparator<_Key, _Compare>()), "");
+    }
+
     _LIBCPP_INLINE_VISIBILITY
           iterator begin() _NOEXCEPT       {return __tree_.begin();}
     _LIBCPP_INLINE_VISIBILITY
diff --git a/libcxx/include/unordered_map b/libcxx/include/unordered_map
--- a/libcxx/include/unordered_map
+++ b/libcxx/include/unordered_map
@@ -852,7 +852,6 @@
     typedef const value_type&                              const_reference;
     static_assert((is_same<value_type, typename allocator_type::value_type>::value),
                   "Invalid allocator::value_type");
-    static_assert(sizeof(__diagnose_unordered_container_requirements<_Key, _Hash, _Pred>(0)), "");
 
 private:
     typedef __hash_value_type<key_type, mapped_type>                 __value_type;
@@ -963,7 +962,11 @@
       const allocator_type& __a)
       : unordered_map(__il, __n, __hf, key_equal(), __a) {}
 #endif
-    // ~unordered_map() = default;
+    _LIBCPP_INLINE_VISIBILITY
+    ~unordered_map() {
+        static_assert(sizeof(__diagnose_unordered_container_requirements<_Key, _Hash, _Pred>(0)), "");
+    }
+
     _LIBCPP_INLINE_VISIBILITY
     unordered_map& operator=(const unordered_map& __u)
     {
@@ -1678,7 +1681,6 @@
     typedef const value_type&                              const_reference;
     static_assert((is_same<value_type, typename allocator_type::value_type>::value),
                   "Invalid allocator::value_type");
-    static_assert(sizeof(__diagnose_unordered_container_requirements<_Key, _Hash, _Pred>(0)), "");
 
 private:
     typedef __hash_value_type<key_type, mapped_type>                 __value_type;
@@ -1787,7 +1789,11 @@
       const allocator_type& __a)
       : unordered_multimap(__il, __n, __hf, key_equal(), __a) {}
 #endif
-    // ~unordered_multimap() = default;
+    _LIBCPP_INLINE_VISIBILITY
+    ~unordered_multimap() {
+        static_assert(sizeof(__diagnose_unordered_container_requirements<_Key, _Hash, _Pred>(0)), "");
+    }
+
     _LIBCPP_INLINE_VISIBILITY
     unordered_multimap& operator=(const unordered_multimap& __u)
     {
diff --git a/libcxx/include/unordered_set b/libcxx/include/unordered_set
--- a/libcxx/include/unordered_set
+++ b/libcxx/include/unordered_set
@@ -390,7 +390,6 @@
     typedef const value_type&                                          const_reference;
     static_assert((is_same<value_type, typename allocator_type::value_type>::value),
                   "Invalid allocator::value_type");
-    static_assert(sizeof(__diagnose_unordered_container_requirements<_Value, _Hash, _Pred>(0)), "");
 
 private:
     typedef __hash_table<value_type, hasher, key_equal, allocator_type> __table;
@@ -486,7 +485,11 @@
         : unordered_set(__il, __n, __hf, key_equal(), __a) {}
 #endif
 #endif  // _LIBCPP_CXX03_LANG
-    // ~unordered_set() = default;
+    _LIBCPP_INLINE_VISIBILITY
+    ~unordered_set() {
+        static_assert(sizeof(__diagnose_unordered_container_requirements<_Value, _Hash, _Pred>(0)), "");
+    }
+
     _LIBCPP_INLINE_VISIBILITY
     unordered_set& operator=(const unordered_set& __u)
     {
@@ -990,7 +993,6 @@
     typedef const value_type&                                          const_reference;
     static_assert((is_same<value_type, typename allocator_type::value_type>::value),
                   "Invalid allocator::value_type");
-    static_assert(sizeof(__diagnose_unordered_container_requirements<_Value, _Hash, _Pred>(0)), "");
 
 private:
     typedef __hash_table<value_type, hasher, key_equal, allocator_type> __table;
@@ -1084,7 +1086,11 @@
       : unordered_multiset(__il, __n, __hf, key_equal(), __a) {}
 #endif
 #endif  // _LIBCPP_CXX03_LANG
-    // ~unordered_multiset() = default;
+    _LIBCPP_INLINE_VISIBILITY
+    ~unordered_multiset() {
+        static_assert(sizeof(__diagnose_unordered_container_requirements<_Value, _Hash, _Pred>(0)), "");
+    }
+
     _LIBCPP_INLINE_VISIBILITY
     unordered_multiset& operator=(const unordered_multiset& __u)
     {
diff --git a/libcxx/test/libcxx/containers/associative/non_const_comparator.pass.cpp b/libcxx/test/libcxx/containers/associative/non_const_comparator.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/libcxx/containers/associative/non_const_comparator.pass.cpp
@@ -0,0 +1,47 @@
+//===----------------------------------------------------------------------===//
+//
+// 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++98, c++03
+// REQUIRES: verify-support
+
+// Test that libc++ does not generate a warning diagnostic about the comparator
+// too early for containers of incomplete types.
+//
+// See PR41360.
+
+#include <set>
+#include <map>
+#include <functional>
+
+
+template <template <typename ...> class Container>
+void test() {
+  struct Base { };
+  struct Derived;  // derives from Base, but incomplete at this point
+
+  // Name the type but don't instantiate it.
+  using C = Container<Derived*, std::less<Base*>>;
+
+  // Instantiate it but don't ODR use any members.
+  typename C::value_type dummy; (void)dummy;
+
+  // Complete the types.
+  struct Derived : Base { };
+
+  C c; // ODR use it, which should be OK
+}
+
+int main(int, char**) {
+  // expected-no-diagnostics
+  test<std::set>();
+  test<std::map>();
+  test<std::multiset>();
+  test<std::multimap>();
+
+  return 0;
+}
diff --git a/libcxx/test/libcxx/containers/unord/non_const_comparator.pass.cpp b/libcxx/test/libcxx/containers/unord/non_const_comparator.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/libcxx/containers/unord/non_const_comparator.pass.cpp
@@ -0,0 +1,47 @@
+//===----------------------------------------------------------------------===//
+//
+// 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++98, c++03
+// REQUIRES: verify-support
+
+// Test that libc++ does not generate a warning diagnostic about the comparator
+// or the hasher too early for containers of incomplete types.
+//
+// See PR41360.
+
+#include <unordered_set>
+#include <unordered_map>
+#include <functional>
+
+
+template <template <typename ...> class Container>
+void test() {
+  struct Base { };
+  struct Derived;  // derives from Base, but incomplete at this point
+
+  // Name the type but don't instantiate it.
+  using C = Container<Derived*, std::less<Base*>, std::hash<Base*>>;
+
+  // Instantiate it but don't ODR use any members.
+  typename C::value_type dummy; (void)dummy;
+
+  // Complete the types.
+  struct Derived : Base { };
+
+  C c; // ODR use it, which should be OK
+}
+
+int main(int, char**) {
+  // expected-no-disagnostics
+  test<std::unordered_set>();
+  test<std::unordered_multiset>();
+  test<std::unordered_map>();
+  test<std::unordered_multimap>();
+
+  return 0;
+}