Index: Lib/test/pickletester.py
===================================================================
--- Lib/test/pickletester.py	(revision 82333)
+++ Lib/test/pickletester.py	(working copy)
@@ -1295,7 +1295,36 @@
         f.seek(0)
         self.assertEqual(unpickler.load(), data2)
 
+    def test_pickling_circular_refs(self):
+        # See issue # 1581183.
+        for proto in protocols:
+            f = io.BytesIO()
+            pickler = self.pickler_class(f, protocol=proto)
+            x = Y().x
+            assert x.a.x is  x
+            pickler.dump(x)
+            pickled = f.getvalue()
 
+            f = io.BytesIO()
+            f.write(pickled)
+            f.seek(0)
+            unpickler = self.unpickler_class(f)
+            x = unpickler.load()
+            self.assertIs(x.a.x, x, "failed for proto=%d" % proto)
+
+class X:
+    def __new__(cls, a):
+        res = object.__new__(cls)
+        res.a = a
+        return res
+    def __getnewargs__(self):
+        return (self.a,)
+
+class Y:
+    def __init__(self):
+        self.x = X(self)
+
+
 if __name__ == "__main__":
     # Print some stuff that can be used to rewrite DATA{0,1,2}
     from pickletools import dis
Index: Lib/pickle.py
===================================================================
--- Lib/pickle.py	(revision 82333)
+++ Lib/pickle.py	(working copy)
@@ -254,10 +254,10 @@
         # growable) array, indexed by memo key.
         if self.fast:
             return
-        assert id(obj) not in self.memo
-        memo_len = len(self.memo)
-        self.write(self.put(memo_len))
-        self.memo[id(obj)] = memo_len, obj
+        if id(obj) not in self.memo:
+            memo_len = len(self.memo)
+            self.write(self.put(memo_len))
+            self.memo[id(obj)] = memo_len, obj
 
     # Return a PUT (BINPUT, LONG_BINPUT) opcode string, with argument i.
     def put(self, i, pack=struct.pack):