@@ -130,11 +130,15 @@ def get_status(self) -> str:
 
 async def connect(self,
 loop: typing.Optional[asyncio.AbstractEventLoop] = None,
-**kwargs: typing.Any) -> 'connection.Connection':
+**kwargs: typing.Any) \
+-> 'connection.Connection[typing.Any]':
 conn_info = typing.cast(typing.Dict[str, typing.Any],
 self.get_connection_spec())
 conn_info.update(kwargs)
-return await asyncpg.connect(loop=loop, **conn_info)
+return typing.cast(
+'connection.Connection[typing.Any]',
+await asyncpg.connect(loop=loop, **conn_info)
+)
 
 def init(self, **settings: str) -> str:
 """Initialize cluster."""

@@ -29,6 +29,7 @@
 
 _Connection = typing.TypeVar('_Connection')
 _Protocol = typing.TypeVar('_Protocol', bound=asyncio.Protocol)
+_Record = typing.TypeVar('_Record', bound=protocol.Record)
 
 _TPTupleType = typing.Tuple[asyncio.WriteTransport, _Protocol]
 AddrType = typing.Union[typing.Tuple[str, int], str]
@@ -654,7 +655,7 @@ async def _connect_addr(
 params: _ConnectionParameters,
 config: _ClientConfiguration,
 connection_class: typing.Type[_Connection],
-record_class: typing.Any
+record_class: typing.Type[_Record]
 ) -> _Connection:
 assert loop is not None
 
@@ -680,7 +681,7 @@ async def _connect_addr(
 assert not params.ssl
 connector = typing.cast(
 typing.Coroutine[typing.Any, None,
-_TPTupleType[protocol.Protocol]],
+_TPTupleType['protocol.Protocol[_Record]']],
 loop.create_unix_connection(proto_factory, addr))
 elif params.ssl:
 connector = _create_ssl_connection(
@@ -689,7 +690,7 @@ async def _connect_addr(
 else:
 connector = typing.cast(
 typing.Coroutine[typing.Any, None,
-_TPTupleType[protocol.Protocol]],
+_TPTupleType['protocol.Protocol[_Record]']],
 loop.create_connection(proto_factory, *addr))
 
 connector_future = asyncio.ensure_future(connector)
@@ -721,7 +722,7 @@ async def _connect(
 loop: typing.Optional[asyncio.AbstractEventLoop],
 timeout: float,
 connection_class: typing.Type[_Connection],
-record_class: typing.Any,
+record_class: typing.Type[_Record],
 **kwargs: typing.Any
 ) -> _Connection:
 if loop is None: