diff --git a/Lib/asyncio/base_events.py b/Lib/asyncio/base_events.py
index b2d446a51fe..d71d6f72bf3 100644
--- a/Lib/asyncio/base_events.py
+++ b/Lib/asyncio/base_events.py
@@ -1525,14 +1525,6 @@ async def connect_accepted_socket(
             self, protocol_factory, sock,
             *, ssl=None,
             ssl_handshake_timeout=None):
-        """Handle an accepted connection.
-
-        This is used by servers that accept connections outside of
-        asyncio but that use asyncio to handle connections.
-
-        This method is a coroutine.  When completed, the coroutine
-        returns a (transport, protocol) pair.
-        """
         if sock.type != socket.SOCK_STREAM:
             raise ValueError(f'A Stream Socket was expected, got {sock!r}')
 
diff --git a/Lib/asyncio/events.py b/Lib/asyncio/events.py
index 0dce87b8ecc..1a20f362ec3 100644
--- a/Lib/asyncio/events.py
+++ b/Lib/asyncio/events.py
@@ -418,6 +418,20 @@ async def create_unix_server(
         """
         raise NotImplementedError
 
+    async def connect_accepted_socket(
+            self, protocol_factory, sock,
+            *, ssl=None,
+            ssl_handshake_timeout=None):
+        """Handle an accepted connection.
+
+        This is used by servers that accept connections outside of
+        asyncio, but use asyncio to handle connections.
+
+        This method is a coroutine.  When completed, the coroutine
+        returns a (transport, protocol) pair.
+        """
+        raise NotImplementedError
+
     async def create_datagram_endpoint(self, protocol_factory,
                                        local_addr=None, remote_addr=None, *,
                                        family=0, proto=0, flags=0,
diff --git a/Misc/NEWS.d/next/Library/2020-07-18-17-39-28.bpo-41332.QRGmA5.rst b/Misc/NEWS.d/next/Library/2020-07-18-17-39-28.bpo-41332.QRGmA5.rst
new file mode 100644
index 00000000000..fa3fb83b9f5
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-07-18-17-39-28.bpo-41332.QRGmA5.rst
@@ -0,0 +1,2 @@
+Added missing connect_accepted_socket() method to
+``asyncio.AbstractEventLoop``.