diff --git a/Doc/library/ssl.rst b/Doc/library/ssl.rst
index 200ab04..eb4d8ac 100644
--- a/Doc/library/ssl.rst
+++ b/Doc/library/ssl.rst
@@ -1593,8 +1593,9 @@
       do_handshake_on_connect=True, suppress_ragged_eofs=True, \
       server_hostname=None, session=None)
 
-   Wrap an existing Python socket *sock* and return an :class:`SSLSocket`
-   object.  *sock* must be a :data:`~socket.SOCK_STREAM` socket; other socket
+   Wrap an existing Python socket *sock* and return an instance of
+   :attr:`SSLContext.sslsocket_class` (default :class:`SSLSocket`).
+   *sock* must be a :data:`~socket.SOCK_STREAM` socket; other socket
    types are unsupported.
 
    The returned SSL socket is tied to the context, its settings and
@@ -1617,12 +1618,25 @@
    .. versionchanged:: 3.6
       *session* argument was added.
 
+    .. versionchanged:: 3.7
+      The method returns on instance of :attr:`SSLContext.sslsocket_class`
+      instead of hard-coded :class:`SSLSocket`.
+
+.. attribute:: SSLContext.sslsocket_class
+
+   The return type of :meth:`SSLContext.wrap_sockets`, defaults to
+   :class:`SSLSocket`. The attribute can be overridden on instance of class
+   in order to return a custom subclass of :class:`SSLSocket`.
+
+   .. versionadded:: 3.7
+
 .. method:: SSLContext.wrap_bio(incoming, outgoing, server_side=False, \
                                 server_hostname=None, session=None)
 
-   Create a new :class:`SSLObject` instance by wrapping the BIO objects
-   *incoming* and *outgoing*. The SSL routines will read input data from the
-   incoming BIO and write data to the outgoing BIO.
+   Wrap the BIO objects *incoming* and *outgoing* and return an instance of
+   attr:`SSLContext.sslobject_class` (default :class:`SSLObject`). The SSL
+   routines will read input data from the incoming BIO and write data to the
+   outgoing BIO.
 
    The *server_side*, *server_hostname* and *session* parameters have the
    same meaning as in :meth:`SSLContext.wrap_socket`.
@@ -1630,6 +1644,18 @@
    .. versionchanged:: 3.6
       *session* argument was added.
 
+   .. versionchanged:: 3.7
+      The method returns on instance of :attr:`SSLContext.sslobject_class`
+      instead of hard-coded :class:`SSLObject`.
+
+.. attribute:: SSLContext.sslobject_class
+
+   The return type of :meth:`SSLContext.wrap_bio`, defaults to
+   :class:`SSLObject`. The attribute can be overridden on instance of class
+   in order to return a custom subclass of :class:`SSLObject`.
+
+   .. versionadded:: 3.7
+
 .. method:: SSLContext.session_stats()
 
    Get statistics about the SSL sessions created or managed by this context.
diff --git a/Lib/ssl.py b/Lib/ssl.py
index 062e802..2849dee 100644
--- a/Lib/ssl.py
+++ b/Lib/ssl.py
@@ -383,10 +383,11 @@
 class SSLContext(_SSLContext):
     """An SSLContext holds various SSL-related configuration options and
     data, such as certificates and possibly a private key."""
-
-    __slots__ = ('protocol', '__weakref__')
     _windows_cert_stores = ("CA", "ROOT")
 
+    sslsocket_class = None  # SSLSocket is assigned later.
+    sslobject_class = None  # SSLObject is assigned later.
+
     def __new__(cls, protocol=PROTOCOL_TLS, *args, **kwargs):
         self = _SSLContext.__new__(cls, protocol)
         if protocol != _SSLv2_IF_EXISTS:
@@ -400,17 +401,21 @@
                     do_handshake_on_connect=True,
                     suppress_ragged_eofs=True,
                     server_hostname=None, session=None):
-        return SSLSocket(sock=sock, server_side=server_side,
-                         do_handshake_on_connect=do_handshake_on_connect,
-                         suppress_ragged_eofs=suppress_ragged_eofs,
-                         server_hostname=server_hostname,
-                         _context=self, _session=session)
+        return self.sslsocket_class(
+            sock=sock,
+            server_side=server_side,
+            do_handshake_on_connect=do_handshake_on_connect,
+            suppress_ragged_eofs=suppress_ragged_eofs,
+            server_hostname=server_hostname,
+            _context=self,
+            _session=session
+        )
 
     def wrap_bio(self, incoming, outgoing, server_side=False,
                  server_hostname=None, session=None):
         sslobj = self._wrap_bio(incoming, outgoing, server_side=server_side,
                                 server_hostname=server_hostname)
-        return SSLObject(sslobj, session=session)
+        return self.sslobject_class(sslobj, session=session)
 
     def set_npn_protocols(self, npn_protocols):
         protos = bytearray()
@@ -1135,6 +1140,11 @@
         return self._sslobj.version()
 
 
+# Python does not support forward declaration of types.
+SSLContext.sslsocket_class = SSLSocket
+SSLContext.sslobject_class = SSLObject
+
+
 def wrap_socket(sock, keyfile=None, certfile=None,
                 server_side=False, cert_reqs=CERT_NONE,
                 ssl_version=PROTOCOL_TLS, ca_certs=None,
diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 523322d..fb5958f 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -1359,6 +1359,22 @@
         self.assertFalse(ctx.check_hostname)
         self.assertEqual(ctx.verify_mode, ssl.CERT_NONE)
 
+    def test_context_custom_class(self):
+        class MySSLSocket(ssl.SSLSocket):
+            pass
+
+        class MySSLObject(ssl.SSLObject):
+            pass
+
+        ctx = ssl.SSLContext(ssl.PROTOCOL_TLS_SERVER)
+        ctx.sslsocket_class = MySSLSocket
+        ctx.sslobject_class = MySSLObject
+
+        with ctx.wrap_socket(socket.socket(), server_side=True) as sock:
+            self.assertIsInstance(sock, MySSLSocket)
+        obj = ctx.wrap_bio(ssl.MemoryBIO(), ssl.MemoryBIO())
+        self.assertIsInstance(obj, MySSLObject)
+
 
 class SSLErrorTests(unittest.TestCase):
 
diff --git a/Misc/NEWS.d/next/Library/2017-09-07-12-15-56.bpo-27629.7xJXEy.rst b/Misc/NEWS.d/next/Library/2017-09-07-12-15-56.bpo-27629.7xJXEy.rst
new file mode 100644
index 0000000..95a6c2b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2017-09-07-12-15-56.bpo-27629.7xJXEy.rst
@@ -0,0 +1,2 @@
+Make return types of SSLContext.wrap_bio() and SSLContext.wrap_socket()
+customizable.