diff --git a/gcc/cp/pt.c b/gcc/cp/pt.c
index 076224c..48f9382 100644
--- a/gcc/cp/pt.c
+++ b/gcc/cp/pt.c
@@ -17224,8 +17224,13 @@ instantiate_decl (tree d, int defer_ok,
   if (!pattern_defined && expl_inst_class_mem_p
       && DECL_EXPLICIT_INSTANTIATION (d))
     {
-      DECL_NOT_REALLY_EXTERN (d) = 0;
-      DECL_INTERFACE_KNOWN (d) = 0;
+      /* Leave linkage flags alone on instantiations with anonymous
+	 visibility.  */
+      if (TREE_PUBLIC (d))
+	{
+	  DECL_NOT_REALLY_EXTERN (d) = 0;
+	  DECL_INTERFACE_KNOWN (d) = 0;
+	}
       SET_DECL_IMPLICIT_INSTANTIATION (d);
     }
 
diff --git a/gcc/testsuite/g++.dg/template/anon5.C b/gcc/testsuite/g++.dg/template/anon5.C
new file mode 100644
index 0000000..34599c0
--- /dev/null
+++ b/gcc/testsuite/g++.dg/template/anon5.C
@@ -0,0 +1,6 @@
+// PR c++/45651
+
+namespace { template <int T> struct A {}; }
+template <int T> struct B { void f(A<T>); };
+template struct B<1>;
+template<int T> void B<T>::f(A<T>) {}