diff --git a/clang/lib/AST/ASTStructuralEquivalence.cpp b/clang/lib/AST/ASTStructuralEquivalence.cpp
index c6df340cbdf0a..20dcaab7d90d3 100644
--- a/clang/lib/AST/ASTStructuralEquivalence.cpp
+++ b/clang/lib/AST/ASTStructuralEquivalence.cpp
@@ -1751,9 +1751,20 @@ static bool IsStructurallyEquivalent(StructuralEquivalenceContext &Context,
   // fulfill the preceding requirements. ... Otherwise, the structure, union,
   // or enumerated types are incompatible.
 
-  if (!NameIsStructurallyEquivalent(*D1, *D2)) {
+  // Note: "the same tag" refers to the identifier for the structure; two
+  // structures without names are not compatible within a TU. In C23, if either
+  // declaration has no name, they're not equivalent. However, the paragraph
+  // after the bulleted list goes on to talk about compatibility of anonymous
+  // structure and union members, so this prohibition only applies to top-level
+  // declarations, not members.
+  if (Context.LangOpts.C23 && (!D1->getIdentifier() || !D2->getIdentifier()) &&
+      (D1->getDeclContext()->isTranslationUnit() ||
+       D2->getDeclContext()->isTranslationUnit()))
+    return false;
+
+  // Otherwise, check the names for equivalence.
+  if (!NameIsStructurallyEquivalent(*D1, *D2))
     return false;
-  }
 
   if (D1->isUnion() != D2->isUnion()) {
     if (Context.Complain) {
diff --git a/clang/test/C/C23/n3037.c b/clang/test/C/C23/n3037.c
index 121b220323e83..03dc78d9c8633 100644
--- a/clang/test/C/C23/n3037.c
+++ b/clang/test/C/C23/n3037.c
@@ -140,7 +140,7 @@ struct quals_matter { // c17-note {{previous definition is here}}
 };
 
 struct quals_matter { // c17-error {{redefinition of 'quals_matter'}} \
-                         c23-error {{type 'struct quals_matter' has incompatible definitions}}                         
+                         c23-error {{type 'struct quals_matter' has incompatible definitions}}
   const int x;        // c23-note {{field 'x' has type 'const int' here}}
 };
 
@@ -359,3 +359,29 @@ struct alignment { // c17-error {{redefinition of 'alignment'}} \
                       c23-error {{type 'struct alignment' has a member with an attribute which currently causes the types to be treated as though they are incompatible}}
   int x;
 };
+
+// Both structures need to have a tag in order to be compatible within the same
+// translation unit.
+struct     {int i;} nontag;
+struct tag {int i;} tagged; // c17-note 2 {{previous definition is here}}
+
+_Static_assert(1 == _Generic(tagged, struct tag {int i;}:1, default:0)); // c17-error {{redefinition of 'tag'}} \
+                                                                            c17-error {{static assertion failed}}
+_Static_assert(0 == _Generic(tagged, struct     {int i;}:1, default:0));
+_Static_assert(0 == _Generic(nontag, struct tag {int i;}:1, default:0)); // c17-error {{redefinition of 'tag'}}
+// That means these two structures are not actually compatible; see GH141724.
+_Static_assert(0 == _Generic(nontag, struct     {int i;}:1, default:0));
+
+struct InnerAnonStruct {
+  struct {
+    int i;
+  } untagged;
+} inner_anon_tagged;
+
+_Static_assert(0 == _Generic(inner_anon_tagged.untagged, struct { int i; } : 1, default : 0));
+
+
+// Test the same thing with enumerations (test for unions is omitted because
+// unions and structures are both RecordDecl objects, whereas EnumDecl is not).
+enum { E_Untagged1 } nontag_enum; // both-note {{previous definition is here}}
+_Static_assert(0 == _Generic(nontag_enum, enum { E_Untagged1 } : 1, default : 0)); // both-error {{redefinition of enumerator 'E_Untagged1'}}