diff --git a/Doc/library/mmap.rst b/Doc/library/mmap.rst
index 5001d4f..e061088 100644
--- a/Doc/library/mmap.rst
+++ b/Doc/library/mmap.rst
@@ -86,6 +86,10 @@
    defaults to 0.  *offset* must be a multiple of the PAGESIZE or
    ALLOCATIONGRANULARITY.
 
+   To ensure validity of the created memory mapping the file specified
+   by the descriptor *fileno* is internally automatically synchronized
+   with physical backing store on Mac OS X and OpenVMS.
+
    This example shows a simple way of using :class:`mmap`::
 
       import mmap
diff --git a/Lib/test/test_zlib.py b/Lib/test/test_zlib.py
index 48ac40a..7593c06 100644
--- a/Lib/test/test_zlib.py
+++ b/Lib/test/test_zlib.py
@@ -74,7 +74,7 @@
         with open(support.TESTFN, "wb+") as f:
             f.seek(_4G)
             f.write(b"asdf")
-        with open(support.TESTFN, "rb") as f:
+            f.flush()
             self.mapping = mmap.mmap(f.fileno(), 0, access=mmap.ACCESS_READ)
 
     def tearDown(self):
diff --git a/Misc/NEWS b/Misc/NEWS
index 67a4bb3..8878612 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -66,6 +66,9 @@
 Library
 -------
 
+- Issue #11277: mmap.mmap() calls fcntl(fd, F_FULLFSYNC) on Mac OS X to get
+  around a mmap bug with sparse files. Patch written by Steffen Daode Nurpmeso.
+
 - Issue #11763: don't use difflib in TestCase.assertMultiLineEqual if the
   strings are too long.
 
diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
index f484a7a..88da4a0 100644
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -23,6 +23,9 @@
 
 #ifndef MS_WINDOWS
 #define UNIX
+# ifdef __APPLE__
+#  include <fcntl.h>
+# endif
 #endif
 
 #ifdef MS_WINDOWS
@@ -1091,6 +1094,12 @@
                             "mmap invalid access parameter.");
     }
 
+#ifdef __APPLE__
+    /* Issue #11277: fsync(2) is not enough on OS X - a special, OS X specific
+       fcntl(2) is necessary to force DISKSYNC and get around mmap(2) bug */
+    if (fd != -1)
+        (void)fcntl(fd, F_FULLFSYNC);
+#endif
 #ifdef HAVE_FSTAT
 #  ifdef __VMS
     /* on OpenVMS we must ensure that all bytes are written to the file */