diff --git a/Lib/test/test_mmap.py b/Lib/test/test_mmap.py
index 86dea1e..047d700 100644
--- a/Lib/test/test_mmap.py
+++ b/Lib/test/test_mmap.py
@@ -1,6 +1,6 @@
-from test.test_support import TESTFN, run_unittest, import_module
+from test.test_support import TESTFN, run_unittest, import_module, unlink, requires
 import unittest
-import os, re, itertools, socket
+import os, re, itertools, socket, sys
 
 mmap = import_module('mmap')
 
@@ -627,8 +627,63 @@
             finally:
                 s.close()
 
+
+class LargeMmapTests(unittest.TestCase):
+
+    def setUp(self):
+        unlink(TESTFN)
+
+    def tearDown(self):
+        unlink(TESTFN)
+
+    def _working_largefile(self):
+        # Only run if the current filesystem supports large files.
+        f = open(TESTFN, 'wb', buffering=0)
+        try:
+            f.seek(0x80000001)
+            f.write(b'x')
+            f.flush()
+        except (IOError, OverflowError):
+            raise unittest.SkipTest("filesystem does not have largefile support")
+        finally:
+            f.close()
+            unlink(TESTFN)
+
+    def test_large_offset(self):
+        if sys.platform[:3] == 'win' or sys.platform == 'darwin':
+            requires('largefile',
+                'test requires %s bytes and a long time to run' % str(0x180000000))
+        self._working_largefile()
+        with open(TESTFN, 'wb') as f:
+            f.seek(0x14FFFFFFF)
+            f.write(b" ")
+
+        with open(TESTFN, 'rb') as f:
+            m = mmap.mmap(f.fileno(), 0, offset=0x140000000, access=mmap.ACCESS_READ)
+            try:
+                self.assertEqual(m[0xFFFFFFF], b" ")
+            finally:
+                m.close()
+
+    def test_large_filesize(self):
+        if sys.platform[:3] == 'win' or sys.platform == 'darwin':
+            requires('largefile',
+                'test requires %s bytes and a long time to run' % str(0x180000000))
+        self._working_largefile()
+        with open(TESTFN, 'wb') as f:
+            f.seek(0x17FFFFFFF)
+            f.write(b" ")
+
+        with open(TESTFN, 'rb') as f:
+            m = mmap.mmap(f.fileno(), 0x10000, access=mmap.ACCESS_READ)
+            try:
+                self.assertEqual(m.size(), 0x180000000)
+            finally:
+                m.close()
+
+
 def test_main():
-    run_unittest(MmapTests)
+    run_unittest(MmapTests, LargeMmapTests)
 
 if __name__ == '__main__':
     test_main()