diff --git a/stdlib/3/asyncio/__init__.pyi b/stdlib/3/asyncio/__init__.pyi
index 885dfce09..cada742b4 100644
--- a/stdlib/3/asyncio/__init__.pyi
+++ b/stdlib/3/asyncio/__init__.pyi
@@ -18,8 +18,6 @@ from asyncio.streams import (
     StreamReaderProtocol as StreamReaderProtocol,
     open_connection as open_connection,
     start_server as start_server,
-    IncompleteReadError as IncompleteReadError,
-    LimitOverrunError as LimitOverrunError,
 )
 from asyncio.subprocess import (
     create_subprocess_exec as create_subprocess_exec,
@@ -35,9 +33,6 @@ from asyncio.transports import (
 )
 from asyncio.futures import (
     Future as Future,
-    CancelledError as CancelledError,
-    TimeoutError as TimeoutError,
-    InvalidStateError as InvalidStateError,
     wrap_future as wrap_future,
 )
 from asyncio.tasks import (
@@ -122,4 +117,27 @@ DefaultEventLoopPolicy: Type[AbstractEventLoopPolicy]
 
 # TODO: AbstractChildWatcher (UNIX only)
 
+if sys.version_info >= (3, 8):
+    from asyncio.exceptions import (
+        CancelledError as CancelledError,
+        IncompleteReadError as IncompleteReadError,
+        InvalidStateError as InvalidStateError,
+        LimitOverrunError as LimitOverrunError,
+        SendfileNotAvailableError as SendfileNotAvailableError,
+        TimeoutError as TimeoutError,
+    )
+else:
+    from asyncio.events import (
+        SendfileNotAvailableError as SendfileNotAvailableError
+    )
+    from asyncio.futures import (
+        CancelledError as CancelledError,
+        TimeoutError as TimeoutError,
+        InvalidStateError as InvalidStateError,
+    )
+    from asyncio.streams import (
+        IncompleteReadError as IncompleteReadError,
+        LimitOverrunError as LimitOverrunError,
+    )
+
 __all__: List[str]
diff --git a/stdlib/3/asyncio/events.pyi b/stdlib/3/asyncio/events.pyi
index 66f7c9f9e..e766d9b08 100644
--- a/stdlib/3/asyncio/events.pyi
+++ b/stdlib/3/asyncio/events.pyi
@@ -303,3 +303,6 @@ def _get_running_loop() -> AbstractEventLoop: ...
 
 if sys.version_info >= (3, 7):
     def get_running_loop() -> AbstractEventLoop: ...
+
+if sys.version_info < (3, 8):
+    class SendfileNotAvailableError(RuntimeError): ...
diff --git a/stdlib/3/asyncio/exceptions.pyi b/stdlib/3/asyncio/exceptions.pyi
new file mode 100644
index 000000000..645481a0a
--- /dev/null
+++ b/stdlib/3/asyncio/exceptions.pyi
@@ -0,0 +1,17 @@
+import sys
+from typing import List, Optional
+
+if sys.version_info >= (3, 8):
+    class CancelledError(BaseException): ...
+    class TimeoutError(Exception): ...
+    class InvalidStateError(Exception): ...
+    class SendfileNotAvailableError(RuntimeError): ...
+    class IncompleteReadError(EOFError):
+        expected: Optional[int]
+        partial: bytes
+        def __init__(self, partial: bytes, expected: Optional[int]) -> None: ...
+    class LimitOverrunError(Exception):
+        consumed: int
+        def __init__(self, message: str, consumed: int) -> None: ...
+
+    __all__: List[str]
diff --git a/stdlib/3/asyncio/futures.pyi b/stdlib/3/asyncio/futures.pyi
index 4ebaa339e..5ce41c23d 100644
--- a/stdlib/3/asyncio/futures.pyi
+++ b/stdlib/3/asyncio/futures.pyi
@@ -2,12 +2,15 @@ import sys
 from typing import Any, Union, Callable, TypeVar, Type, List, Iterable, Generator, Awaitable, Optional, Tuple
 from .events import AbstractEventLoop
 from concurrent.futures import (
-    CancelledError as CancelledError,
-    TimeoutError as TimeoutError,
     Future as _ConcurrentFuture,
     Error,
 )
 
+if sys.version_info < (3, 8):
+    from concurrent.futures import CancelledError as CancelledError
+    from concurrent.futures import TimeoutError as TimeoutError
+    class InvalidStateError(Error): ...
+
 if sys.version_info >= (3, 7):
     from contextvars import Context
 
@@ -16,8 +19,6 @@ __all__: List[str]
 _T = TypeVar('_T')
 _S = TypeVar('_S')
 
-class InvalidStateError(Error): ...
-
 class _TracebackLogger:
     exc: BaseException
     tb: List[str]
diff --git a/stdlib/3/asyncio/streams.pyi b/stdlib/3/asyncio/streams.pyi
index 68271c0fe..e1ce96404 100644
--- a/stdlib/3/asyncio/streams.pyi
+++ b/stdlib/3/asyncio/streams.pyi
@@ -11,14 +11,15 @@ _ClientConnectedCallback = Callable[[StreamReader, StreamWriter], Optional[Await
 
 __all__: List[str]
 
-class IncompleteReadError(EOFError):
-    expected: Optional[int]
-    partial: bytes
-    def __init__(self, partial: bytes, expected: Optional[int]) -> None: ...
+if sys.version_info < (3, 8):
+    class IncompleteReadError(EOFError):
+        expected: Optional[int]
+        partial: bytes
+        def __init__(self, partial: bytes, expected: Optional[int]) -> None: ...
 
-class LimitOverrunError(Exception):
-    consumed: int
-    def __init__(self, message: str, consumed: int) -> None: ...
+    class LimitOverrunError(Exception):
+        consumed: int
+        def __init__(self, message: str, consumed: int) -> None: ...
 
 @coroutines.coroutine
 def open_connection(