diff --git a/clang/lib/Parse/ParseDecl.cpp b/clang/lib/Parse/ParseDecl.cpp
--- a/clang/lib/Parse/ParseDecl.cpp
+++ b/clang/lib/Parse/ParseDecl.cpp
@@ -3448,12 +3448,12 @@
         continue;
       }
 
-      if (TemplateId && TemplateId->Kind == TNK_Concept_template &&
-          GetLookAheadToken(2).isOneOf(tok::kw_auto, tok::kw_decltype)) {
+      if (TemplateId && TemplateId->Kind == TNK_Concept_template) {
         DS.getTypeSpecScope() = SS;
-        // This is a qualified placeholder-specifier, e.g., ::C<int> auto ...
-        // Consume the scope annotation and continue to consume the template-id
-        // as a placeholder-specifier.
+        // This is probably a qualified placeholder-specifier, e.g., ::C<int>
+        // auto ... Consume the scope annotation and continue to consume the
+        // template-id as a placeholder-specifier. Let the next iteration
+        // diagnose a missing auto.
         ConsumeAnnotationToken();
         continue;
       }
diff --git a/clang/lib/Parse/Parser.cpp b/clang/lib/Parse/Parser.cpp
--- a/clang/lib/Parse/Parser.cpp
+++ b/clang/lib/Parse/Parser.cpp
@@ -1883,31 +1883,25 @@
       return ANK_TemplateName;
     }
     [[fallthrough]];
+  case Sema::NC_Concept:
   case Sema::NC_VarTemplate:
   case Sema::NC_FunctionTemplate:
   case Sema::NC_UndeclaredTemplate: {
-    // We have a type, variable or function template followed by '<'.
-    ConsumeToken();
-    UnqualifiedId Id;
-    Id.setIdentifier(Name, NameLoc);
-    if (AnnotateTemplateIdToken(
-            TemplateTy::make(Classification.getTemplateName()),
-            Classification.getTemplateNameKind(), SS, SourceLocation(), Id))
-      return ANK_Error;
-    return ANK_Success;
-  }
-  case Sema::NC_Concept: {
-    UnqualifiedId Id;
-    Id.setIdentifier(Name, NameLoc);
+    bool IsConceptName = Classification.getKind() == Sema::NC_Concept;
+    // We have a template name followed by '<'. Consume the identifier token so
+    // we reach the '<' and annotate it.
     if (Next.is(tok::less))
-      // We have a concept name followed by '<'. Consume the identifier token so
-      // we reach the '<' and annotate it.
       ConsumeToken();
+    UnqualifiedId Id;
+    Id.setIdentifier(Name, NameLoc);
     if (AnnotateTemplateIdToken(
             TemplateTy::make(Classification.getTemplateName()),
             Classification.getTemplateNameKind(), SS, SourceLocation(), Id,
-            /*AllowTypeAnnotation=*/false, /*TypeConstraint=*/true))
+            /*AllowTypeAnnotation=*/!IsConceptName,
+            /*TypeConstraint=*/IsConceptName))
       return ANK_Error;
+    if (SS.isNotEmpty())
+      AnnotateScopeToken(SS, !WasScopeAnnotation);
     return ANK_Success;
   }
   }
diff --git a/clang/test/Parser/cxx-template-template-recovery.cpp b/clang/test/Parser/cxx-template-template-recovery.cpp
new file mode 100644
--- /dev/null
+++ b/clang/test/Parser/cxx-template-template-recovery.cpp
@@ -0,0 +1,40 @@
+// RUN: %clang_cc1 -std=c++20 -verify -fsyntax-only %s
+
+namespace a {
+  template <typename T>
+  concept C1 = true; //expected-note {{here}}
+
+  template <typename T>
+  auto V1 = true; //expected-note {{here}}
+
+  namespace b {
+    template <typename T>
+    concept C2 = true; //expected-note {{here}}
+
+    template <typename T>
+    auto V2 = true; //expected-note {{here}}
+  }
+}
+
+template <typename T>
+concept C3 = true; //expected-note {{here}}
+template <typename T>
+auto V3 = true; //expected-note {{here}}
+
+template <template <typename T> typename C>
+constexpr bool test = true;
+
+static_assert(test<a::C1>); //expected-error {{too few template arguments for concept 'C1'}}
+static_assert(test<a::b::C2>); //expected-error {{too few template arguments for concept 'C2'}}
+static_assert(test<C3>); //expected-error {{too few template arguments for concept 'C3'}}
+
+static_assert(test<a::V1>); //expected-error {{use of variable template 'V1' requires template arguments}}
+static_assert(test<a::b::V2>); //expected-error {{use of variable template 'V2' requires template arguments}}
+static_assert(test<V3>); //expected-error {{use of variable template 'V3' requires template arguments}}
+
+
+void f() {
+    C3 t1 = 0;  // expected-error{{expected 'auto' or 'decltype(auto)' after concept name}}
+    a::C1 t2 = 0; // expected-error{{expected 'auto' or 'decltype(auto)' after concept name}}
+    a::b::C2 t3 = 0; // expected-error{{expected 'auto' or 'decltype(auto)' after concept name}}
+}