diff --git a/Lib/pickle.py b/Lib/pickle.py
index 299de16..5d0aba7 100644
--- a/Lib/pickle.py
+++ b/Lib/pickle.py
@@ -427,6 +427,14 @@
         self.write(NONE)
     dispatch[NoneType] = save_none
 
+    def save_ellipsis(self, obj):
+        self.save_global(Ellipsis, 'Ellipsis')
+    dispatch[type(Ellipsis)] = save_ellipsis
+
+    def save_notimplemented(self, obj):
+        self.save_global(NotImplemented, 'NotImplemented')
+    dispatch[type(NotImplemented)] = save_notimplemented
+
     def save_bool(self, obj):
         if self.proto >= 2:
             self.write(obj and NEWTRUE or NEWFALSE)
@@ -770,7 +778,18 @@
     dispatch[ClassType] = save_global
     dispatch[FunctionType] = save_global
     dispatch[BuiltinFunctionType] = save_global
-    dispatch[TypeType] = save_global
+
+    def save_type(self, obj):
+        if obj is type(None):
+            return self.save_reduce(type, (None,), obj=obj)
+        elif obj is type(NotImplemented):
+            return self.save_reduce(type, (NotImplemented,), obj=obj)
+        elif obj is type(Ellipsis):
+            return self.save_reduce(type, (Ellipsis,), obj=obj)
+        return self.save_global(obj)
+
+    dispatch[TypeType] = save_type
+
 
 # Pickling helpers
 
diff --git a/Lib/test/pickletester.py b/Lib/test/pickletester.py
index 1599893..d7b68db 100644
--- a/Lib/test/pickletester.py
+++ b/Lib/test/pickletester.py
@@ -661,6 +661,15 @@
                 u = self.loads(s)
                 self.assertEqual(t, u)
 
+    def test_singleton_types(self):
+        # Issue #6477: Test that types of built-in singletons can be pickled.
+        singletons = [None, Ellipsis, NotImplemented]
+        for singleton in singletons:
+            for proto in protocols:
+                s = self.dumps(type(singleton), proto)
+                u = self.loads(s)
+                self.assertIs(type(singleton), u)
+
     # Tests for protocol 2
 
     def test_proto(self):