diff --git a/Lib/test/test_fileio.py b/Lib/test/test_fileio.py
index 103365d..3588fb4 100644
--- a/Lib/test/test_fileio.py
+++ b/Lib/test/test_fileio.py
@@ -305,6 +305,11 @@
         finally:
             os.unlink(TESTFN)
 
+    def testConstructorHandlesNULChars(self):
+        fn_with_NUL = 'foo\0bar'
+        self.assertRaises(TypeError, _FileIO, fn_with_NUL, 'w')
+        self.assertRaises(TypeError, _FileIO, bytes(fn_with_NUL, 'ascii'), 'w')
+
     def testInvalidFd(self):
         self.assertRaises(ValueError, _FileIO, -10)
         self.assertRaises(OSError, _FileIO, make_bad_fd())
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index df7ca15..ea82cea 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -363,6 +363,11 @@
             self.assertRaises(exc, fp.seek, 1, self.SEEK_CUR)
             self.assertRaises(exc, fp.seek, -1, self.SEEK_END)
 
+    def test_open_handles_NUL_chars(self):
+        fn_with_NUL = 'foo\0bar'
+        self.assertRaises(TypeError, self.open, fn_with_NUL, 'w')
+        self.assertRaises(TypeError, self.open, bytes(fn_with_NUL, 'ascii'), 'w')
+
     def test_raw_file_io(self):
         with self.open(support.TESTFN, "wb", buffering=0) as f:
             self.assertEqual(f.readable(), False)