diff --git a/clang/lib/AST/ASTStructuralEquivalence.cpp b/clang/lib/AST/ASTStructuralEquivalence.cpp
--- a/clang/lib/AST/ASTStructuralEquivalence.cpp
+++ b/clang/lib/AST/ASTStructuralEquivalence.cpp
@@ -235,12 +235,21 @@
 static bool IsStructurallyEquivalent(StructuralEquivalenceContext &Context,
                                      const TemplateName &N1,
                                      const TemplateName &N2) {
-  if (N1.getKind() != N2.getKind())
+  TemplateDecl *TemplateDeclN1 = N1.getAsTemplateDecl();
+  TemplateDecl *TemplateDeclN2 = N2.getAsTemplateDecl();
+  if (TemplateDeclN1 && TemplateDeclN2) {
+    if (!IsStructurallyEquivalent(Context, TemplateDeclN1, TemplateDeclN2))
+      return false;
+    // If the kind is different we compare only the template decl.
+    if (N1.getKind() != N2.getKind())
+      return true;
+  } else if (TemplateDeclN1 || TemplateDeclN2)
     return false;
+  else if (N1.getKind() != N2.getKind())
+    return false;
+
+  // Check for special case incompatibilities.
   switch (N1.getKind()) {
-  case TemplateName::Template:
-    return IsStructurallyEquivalent(Context, N1.getAsTemplateDecl(),
-                                    N2.getAsTemplateDecl());
 
   case TemplateName::OverloadedTemplate: {
     OverloadedTemplateStorage *OS1 = N1.getAsOverloadedTemplate(),
@@ -259,14 +268,6 @@
     return TN1->getDeclName() == TN2->getDeclName();
   }
 
-  case TemplateName::QualifiedTemplate: {
-    QualifiedTemplateName *QN1 = N1.getAsQualifiedTemplateName(),
-                          *QN2 = N2.getAsQualifiedTemplateName();
-    return IsStructurallyEquivalent(Context, QN1->getDecl(), QN2->getDecl()) &&
-           IsStructurallyEquivalent(Context, QN1->getQualifier(),
-                                    QN2->getQualifier());
-  }
-
   case TemplateName::DependentTemplate: {
     DependentTemplateName *DN1 = N1.getAsDependentTemplateName(),
                           *DN2 = N2.getAsDependentTemplateName();
@@ -281,15 +282,6 @@
     return false;
   }
 
-  case TemplateName::SubstTemplateTemplateParm: {
-    SubstTemplateTemplateParmStorage *TS1 = N1.getAsSubstTemplateTemplateParm(),
-                                     *TS2 = N2.getAsSubstTemplateTemplateParm();
-    return IsStructurallyEquivalent(Context, TS1->getParameter(),
-                                    TS2->getParameter()) &&
-           IsStructurallyEquivalent(Context, TS1->getReplacement(),
-                                    TS2->getReplacement());
-  }
-
   case TemplateName::SubstTemplateTemplateParmPack: {
     SubstTemplateTemplateParmPackStorage
         *P1 = N1.getAsSubstTemplateTemplateParmPack(),
@@ -299,8 +291,16 @@
            IsStructurallyEquivalent(Context, P1->getParameterPack(),
                                     P2->getParameterPack());
   }
+
+   case TemplateName::Template:
+   case TemplateName::QualifiedTemplate:
+   case TemplateName::SubstTemplateTemplateParm:
+     // It is sufficient to check value of getAsTemplateDecl.
+     break;
+
   }
-  return false;
+
+  return true;
 }
 
 /// Determine whether two template arguments are equivalent.
diff --git a/clang/unittests/AST/StructuralEquivalenceTest.cpp b/clang/unittests/AST/StructuralEquivalenceTest.cpp
--- a/clang/unittests/AST/StructuralEquivalenceTest.cpp
+++ b/clang/unittests/AST/StructuralEquivalenceTest.cpp
@@ -892,6 +892,67 @@
   EXPECT_FALSE(testStructuralMatch(First, Second));
 }
 
+TEST_F(StructuralEquivalenceTemplateTest,
+       TemplateVsSubstTemplateTemplateParmInArgEq) {
+  auto t = makeDecls<ClassTemplateSpecializationDecl>(
+      R"(
+template <typename P1> class Arg { };
+template <template <typename PP1> class P1> class Primary { };
+
+void f() {
+  // Make specialization with simple template.
+  Primary <Arg> A;
+}
+      )",
+      R"(
+template <typename P1> class Arg { };
+template <template <typename PP1> class P1> class Primary { };
+
+template <template <typename PP1> class P1> class Templ {
+  void f() {
+    // Make specialization with substituted template template param.
+    Primary <P1> A;
+  };
+};
+
+// Instantiate with substitution Arg into P1.
+template class Templ <Arg>;
+      )",
+      Lang_CXX, classTemplateSpecializationDecl(hasName("Primary")));
+  EXPECT_TRUE(testStructuralMatch(t));
+}
+
+TEST_F(StructuralEquivalenceTemplateTest,
+       TemplateVsSubstTemplateTemplateParmInArgNotEq) {
+  auto t = makeDecls<ClassTemplateSpecializationDecl>(
+      R"(
+template <typename P1> class Arg { };
+template <template <typename PP1> class P1> class Primary { };
+
+void f() {
+  // Make specialization with simple template.
+  Primary <Arg> A;
+}
+      )",
+      R"(
+// Arg is different from the other, this should cause non-equivalence.
+template <typename P1> class Arg { int X; };
+template <template <typename PP1> class P1> class Primary { };
+
+template <template <typename PP1> class P1> class Templ {
+  void f() {
+    // Make specialization with substituted template template param.
+    Primary <P1> A;
+  };
+};
+
+// Instantiate with substitution Arg into P1.
+template class Templ <Arg>;
+      )",
+      Lang_CXX, classTemplateSpecializationDecl(hasName("Primary")));
+  EXPECT_FALSE(testStructuralMatch(t));
+}
+
 struct StructuralEquivalenceDependentTemplateArgsTest
     : StructuralEquivalenceTemplateTest {};
 
@@ -1030,5 +1091,111 @@
   EXPECT_FALSE(testStructuralMatch(t));
 }
 
+TEST_F(
+    StructuralEquivalenceTemplateTest,
+    ClassTemplSpecWithQualifiedAndNonQualifiedTypeArgsShouldBeEqual) {
+  auto t = makeDecls<ClassTemplateSpecializationDecl>(
+      R"(
+      template <class T> struct Primary {};
+      namespace N {
+        struct Arg;
+      }
+      // Explicit instantiation with qualified name.
+      template struct Primary<N::Arg>;
+      )",
+      R"(
+      template <class T> struct Primary {};
+      namespace N {
+        struct Arg;
+      }
+      using namespace N;
+      // Explicit instantiation with UNqualified name.
+      template struct Primary<Arg>;
+      )",
+      Lang_CXX,
+      classTemplateSpecializationDecl(hasName("Primary")));
+  EXPECT_TRUE(testStructuralMatch(t));
+}
+
+TEST_F(
+    StructuralEquivalenceTemplateTest,
+    ClassTemplSpecWithInequivalentQualifiedAndNonQualifiedTypeArgs) {
+  auto t = makeDecls<ClassTemplateSpecializationDecl>(
+      R"(
+      template <class T> struct Primary {};
+      namespace N {
+        struct Arg { int a; };
+      }
+      // Explicit instantiation with qualified name.
+      template struct Primary<N::Arg>;
+      )",
+      R"(
+      template <class T> struct Primary {};
+      namespace N {
+        // This struct is not equivalent with the other in the prev TU.
+        struct Arg { double b; }; // -- Field mismatch.
+      }
+      using namespace N;
+      // Explicit instantiation with UNqualified name.
+      template struct Primary<Arg>;
+      )",
+      Lang_CXX,
+      classTemplateSpecializationDecl(hasName("Primary")));
+  EXPECT_FALSE(testStructuralMatch(t));
+}
+
+TEST_F(
+    StructuralEquivalenceTemplateTest,
+    ClassTemplSpecWithQualifiedAndNonQualifiedTemplArgsShouldBeEqual) {
+  auto t = makeDecls<ClassTemplateSpecializationDecl>(
+      R"(
+      template <template <class> class T> struct Primary {};
+      namespace N {
+        template <class T> struct Arg;
+      }
+      // Explicit instantiation with qualified name.
+      template struct Primary<N::Arg>;
+      )",
+      R"(
+      template <template <class> class T> struct Primary {};
+      namespace N {
+        template <class T> struct Arg;
+      }
+      using namespace N;
+      // Explicit instantiation with UNqualified name.
+      template struct Primary<Arg>;
+      )",
+      Lang_CXX,
+      classTemplateSpecializationDecl(hasName("Primary")));
+  EXPECT_TRUE(testStructuralMatch(t));
+}
+
+TEST_F(
+    StructuralEquivalenceTemplateTest,
+    ClassTemplSpecWithInequivalentQualifiedAndNonQualifiedTemplArgs) {
+  auto t = makeDecls<ClassTemplateSpecializationDecl>(
+      R"(
+      template <template <class> class T> struct Primary {};
+      namespace N {
+        template <class T> struct Arg { int a; };
+      }
+      // Explicit instantiation with qualified name.
+      template struct Primary<N::Arg>;
+      )",
+      R"(
+      template <template <class> class T> struct Primary {};
+      namespace N {
+        // This template is not equivalent with the other in the prev TU.
+        template <class T> struct Arg { double b; }; // -- Field mismatch.
+      }
+      using namespace N;
+      // Explicit instantiation with UNqualified name.
+      template struct Primary<Arg>;
+      )",
+      Lang_CXX,
+      classTemplateSpecializationDecl(hasName("Primary")));
+  EXPECT_FALSE(testStructuralMatch(t));
+}
+
 } // end namespace ast_matchers
 } // end namespace clang