diff --git a/stdlib/2/time.pyi b/stdlib/2/time.pyi
index 79f252637..6f234f2a2 100644
--- a/stdlib/2/time.pyi
+++ b/stdlib/2/time.pyi
@@ -1,7 +1,7 @@
 """Stub file for the 'time' module."""
 # See https://docs.python.org/2/library/time.html
 
-from typing import NamedTuple, Tuple, Union, Any
+from typing import NamedTuple, Tuple, Union, Any, Optional
 
 # ----- variables and constants -----
 accept2dyear = False
@@ -25,12 +25,12 @@ def asctime(t: struct_time = ...) -> str:
 
 def clock() -> float: ...
 
-def ctime(secs: float = ...) -> str:
+def ctime(secs: Optional[float] = ...) -> str:
     raise ValueError()
 
-def gmtime(secs: float = ...) -> struct_time: ...
+def gmtime(secs: Optional[float] = ...) -> struct_time: ...
 
-def localtime(secs: float = ...) -> struct_time: ...
+def localtime(secs: Optional[float] = ...) -> struct_time: ...
 
 def mktime(t: struct_time) -> float:
     raise OverflowError()