diff --git a/stdlib/3.4/asyncio/protocols.pyi b/stdlib/3.4/asyncio/protocols.pyi
index 9fcff65c0..a716af7ef 100644
--- a/stdlib/3.4/asyncio/protocols.pyi
+++ b/stdlib/3.4/asyncio/protocols.pyi
@@ -1,5 +1,5 @@
 from asyncio import transports
-from typing import AnyStr, List, Tuple
+from typing import List, Text, Tuple, Union
 
 __all__: List[str]
 
@@ -15,10 +15,10 @@ class Protocol(BaseProtocol):
     def eof_received(self) -> bool: ...
 
 class DatagramProtocol(BaseProtocol):
-    def datagram_received(self, data: AnyStr, addr: Tuple[str, int]) -> None: ...
+    def datagram_received(self, data: Union[bytes, Text], addr: Tuple[str, int]) -> None: ...
     def error_received(self, exc: Exception) -> None: ...
 
 class SubprocessProtocol(BaseProtocol):
-    def pipe_data_received(self, fd: int, data: AnyStr) -> None: ...
+    def pipe_data_received(self, fd: int, data: Union[bytes, Text]) -> None: ...
     def pipe_connection_lost(self, fd: int, exc: Exception) -> None: ...
     def process_exited(self) -> None: ...
diff --git a/stdlib/3.4/asyncio/subprocess.pyi b/stdlib/3.4/asyncio/subprocess.pyi
index 78feb8e20..ab2ecd8d8 100644
--- a/stdlib/3.4/asyncio/subprocess.pyi
+++ b/stdlib/3.4/asyncio/subprocess.pyi
@@ -3,7 +3,7 @@ from asyncio import protocols
 from asyncio import streams
 from asyncio import transports
 from asyncio.coroutines import coroutine
-from typing import Any, AnyStr, Generator, List, Optional, Tuple, Union, IO
+from typing import Any, Generator, List, Optional, Text, Tuple, Union, IO
 
 __all__: List[str]
 
@@ -18,7 +18,7 @@ class SubprocessStreamProtocol(streams.FlowControlMixin,
     stderr = ...  # type: Optional[streams.StreamReader]
     def __init__(self, limit: int, loop: events.AbstractEventLoop) -> None: ...
     def connection_made(self, transport: transports.BaseTransport) -> None: ...
-    def pipe_data_received(self, fd: int, data: AnyStr) -> None: ...
+    def pipe_data_received(self, fd: int, data: Union[bytes, Text]) -> None: ...
     def pipe_connection_lost(self, fd: int, exc: Exception) -> None: ...
     def process_exited(self) -> None: ...