diff --git a/Doc/library/mmap.rst b/Doc/library/mmap.rst
index 12b14d69332d72a..b3c0d6fcba56490 100644
--- a/Doc/library/mmap.rst
+++ b/Doc/library/mmap.rst
@@ -81,7 +81,11 @@ To map anonymous memory, -1 should be passed as the fileno along with the length
    private copy-on-write mapping, so changes to the contents of the mmap
    object will be private to this process, and :const:`MAP_SHARED` creates a
    mapping that's shared with all other processes mapping the same areas of
-   the file.  The default value is :const:`MAP_SHARED`.
+   the file. :const:`MAP_ALIGNED_SUPER` (FreeBSD only) uses super pages
+   feature, it is enabled by default in most of architectures and exists
+   since 2008.
+   The default value is :const:`MAP_SHARED`.
+   See :ref:`MAP_* constants <mmap-constants>`.
 
    *prot*, if specified, gives the desired memory protection; the two most
    useful values are :const:`PROT_READ` and :const:`PROT_WRITE`, to specify
@@ -307,6 +311,24 @@ To map anonymous memory, -1 should be passed as the fileno along with the length
       the mmap was created with :const:`ACCESS_READ`, then writing to it will
       raise a :exc:`TypeError` exception.
 
+.. _mmap-constants:
+
+MAP_* Constants
++++++++++++++++
+
+.. data:: MAP_ANONYMOUS
+          MAP_ANON
+          MAP_SHARED
+          MAP_PRIVATE
+          MAP_DENYWRITE
+          MAP_EXECUTABLE
+          MAP_ALIGNED_SUPER
+          MAP_CONCEAL
+
+   .. versionadded:: 3.9
+      Add :data:`MAP_ALIGNED_SUPER` constant.
+      Add :data:`MAP_CONCEAL` constant,
+
 .. _madvise-constants:
 
 MADV_* Constants
@@ -341,3 +363,4 @@ MADV_* Constants
    Availability: Systems with the madvise() system call.
 
    .. versionadded:: 3.8
+
diff --git a/Misc/NEWS.d/next/Library/2019-07-01-14-27-17.bpo-37471._EFODL.rst b/Misc/NEWS.d/next/Library/2019-07-01-14-27-17.bpo-37471._EFODL.rst
new file mode 100644
index 000000000000000..3db2cb573c7a76c
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-07-01-14-27-17.bpo-37471._EFODL.rst
@@ -0,0 +1,2 @@
+Adding new :data:`mmap.MAP_ALIGNED_SUPER` FreeBSD constant.
+Adding new :data:`mmap.MAP_CONCEAL` OpenBSD constant.
diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
index 9e3414f94e3124b..3daaa0b8127fb1b 100644
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -1528,6 +1528,12 @@ PyInit_mmap(void)
     setint(dict, "MAP_ANON", MAP_ANONYMOUS);
     setint(dict, "MAP_ANONYMOUS", MAP_ANONYMOUS);
 #endif
+#ifdef MAP_ALIGNED_SUPER
+    setint(dict, "MAP_ALIGNED_SUPER", MAP_ALIGNED_SUPER);
+#endif
+#ifdef MAP_CONCEAL
+    setint(dict, "MAP_CONCEAL", MAP_CONCEAL);
+#endif
 
     setint(dict, "PAGESIZE", (long)my_getpagesize());