diff --git a/stdlib/3.4/asyncio/events.pyi b/stdlib/3.4/asyncio/events.pyi
index bcac004cb..afdd6397e 100644
--- a/stdlib/3.4/asyncio/events.pyi
+++ b/stdlib/3.4/asyncio/events.pyi
@@ -1,4 +1,4 @@
-from typing import Any, Awaitable, TypeVar, List, Callable, Tuple, Union, Dict
+from typing import Any, Awaitable, TypeVar, List, Callable, Tuple, Union, Dict, Generator
 from abc import ABCMeta, abstractmethod
 from asyncio.futures import Future
 
@@ -34,7 +34,7 @@ class AbstractEventLoop(metaclass=ABCMeta):
     @abstractmethod
     def run_forever(self) -> None: ...
     @abstractmethod
-    def run_until_complete(self, future: Union[Awaitable[_T], Future[_T]]) -> _T: ...
+    def run_until_complete(self, future: Union[Awaitable[_T], Future[_T], Generator[Any, Any, _T]]) -> _T: ...
     @abstractmethod
     def stop(self) -> None: ...
     @abstractmethod
diff --git a/stdlib/3.4/asyncio/tasks.pyi b/stdlib/3.4/asyncio/tasks.pyi
index 9d5dc7aa2..3adebe1ba 100644
--- a/stdlib/3.4/asyncio/tasks.pyi
+++ b/stdlib/3.4/asyncio/tasks.pyi
@@ -1,4 +1,4 @@
-from typing import Any, Iterable, TypeVar, Set, Dict, List, TextIO, Union, Tuple, Generic, Callable
+from typing import Any, Iterable, TypeVar, Set, Dict, List, TextIO, Union, Tuple, Generic, Callable, Generator
 from asyncio.events import AbstractEventLoop
 from asyncio.futures import Future
 # __all__ = ['iscoroutinefunction', 'iscoroutine',
@@ -18,7 +18,7 @@ def coroutine(f: _T) -> _T: ...  # Here comes and go a function
 def sleep(delay: float, result: _T = ..., loop: AbstractEventLoop = ...) -> Future[_T]: ...
 def wait(fs: List[Task[_T]], *, loop: AbstractEventLoop = ...,
     timeout: float = ..., return_when: str = ...) -> Future[Tuple[Set[Future[_T]], Set[Future[_T]]]]: ...
-def wait_for(fut: Future[_T], timeout: float, *, loop: AbstractEventLoop = ...) -> Future[_T]: ...
+def wait_for(fut: Union[Future[_T], Generator[Any, None, _T]], timeout: float, *, loop: AbstractEventLoop = ...) -> Future[_T]: ...
 
 
 class Task(Future[_T], Generic[_T]):
@@ -28,7 +28,7 @@ class Task(Future[_T], Generic[_T]):
     def current_task(cls, loop: AbstractEventLoop = ...) -> Task: ...
     @classmethod
     def all_tasks(cls, loop: AbstractEventLoop = ...) -> Set[Task]: ...
-    def __init__(self, coro: Future[_T], *, loop: AbstractEventLoop = ...) -> None: ...
+    def __init__(self, coro: Union[Future[_T], Generator[Any, None, _T]], *, loop: AbstractEventLoop = ...) -> None: ...
     def __repr__(self) -> str: ...
     def get_stack(self, *, limit: int = ...) -> List[Any]: ...  # return List[stackframe]
     def print_stack(self, *, limit: int = ..., file: TextIO = ...) -> None: ...