diff --git a/Lib/test/test_int.py b/Lib/test/test_int.py
index ec57842b688..6e611c2cc93 100644
--- a/Lib/test/test_int.py
+++ b/Lib/test/test_int.py
@@ -175,6 +175,12 @@ def test_basic(self):
         self.assertEqual(int(' 0O123   ', 0), 83)
         self.assertEqual(int(' 0X123  ', 0), 291)
         self.assertEqual(int(' 0B100 ', 0), 4)
+        self.assertEqual(int('0', 0), 0)
+        self.assertEqual(int('+0', 0), 0)
+        self.assertEqual(int('-0', 0), 0)
+        self.assertEqual(int('00', 0), 0)
+        self.assertRaises(ValueError, int, '08', 0)
+        self.assertRaises(ValueError, int, '-012395', 0)
 
         # without base still base 10
         self.assertEqual(int('0123'), 123)
diff --git a/Lib/test/test_long.py b/Lib/test/test_long.py
index 7be89fcf160..412ec7c5251 100644
--- a/Lib/test/test_long.py
+++ b/Lib/test/test_long.py
@@ -356,6 +356,23 @@ def test_long(self):
         self.assertRaises(ValueError, long, '53', 40)
         self.assertRaises(TypeError, long, 1, 12)
 
+        # tests with base 0
+        self.assertEqual(long(' 0123  ', 0), 83)
+        self.assertEqual(long(' 0123  ', 0), 83)
+        self.assertEqual(long('000', 0), 0)
+        self.assertEqual(long('0o123', 0), 83)
+        self.assertEqual(long('0x123', 0), 291)
+        self.assertEqual(long('0b100', 0), 4)
+        self.assertEqual(long(' 0O123   ', 0), 83)
+        self.assertEqual(long(' 0X123  ', 0), 291)
+        self.assertEqual(long(' 0B100 ', 0), 4)
+        self.assertEqual(long('0', 0), 0)
+        self.assertEqual(long('+0', 0), 0)
+        self.assertEqual(long('-0', 0), 0)
+        self.assertEqual(long('00', 0), 0)
+        self.assertRaises(ValueError, long, '08', 0)
+        self.assertRaises(ValueError, long, '-012395', 0)
+
         # SF patch #1638879: embedded NULs were not detected with
         # explicit base
         self.assertRaises(ValueError, long, '123\0', 10)