diff --git a/asyncpg/connection.py b/asyncpg/connection.py
index 3a86466c..fe9412ab 100644
--- a/asyncpg/connection.py
+++ b/asyncpg/connection.py
@@ -311,7 +311,12 @@ def is_in_transaction(self):
         """
         return self._protocol.is_in_transaction()
 
-    async def execute(self, query: str, *args, timeout: float=None) -> str:
+    async def execute(
+        self,
+        query: str,
+        *args,
+        timeout: typing.Optional[float]=None,
+    ) -> str:
         """Execute an SQL command (or commands).
 
         This method can execute many SQL commands at once, when no arguments
@@ -358,7 +363,13 @@ async def execute(self, query: str, *args, timeout: float=None) -> str:
         )
         return status.decode()
 
-    async def executemany(self, command: str, args, *, timeout: float=None):
+    async def executemany(
+        self,
+        command: str,
+        args,
+        *,
+        timeout: typing.Optional[float]=None,
+    ):
         """Execute an SQL *command* for each sequence of arguments in *args*.
 
         Example:
@@ -757,7 +768,12 @@ async def fetchrow(
         return data[0]
 
     async def fetchmany(
-        self, query, args, *, timeout: float=None, record_class=None
+        self,
+        query,
+        args,
+        *,
+        timeout: typing.Optional[float]=None,
+        record_class=None,
     ):
         """Run a query for each sequence of arguments in *args*
         and return the results as a list of :class:`Record`.
diff --git a/asyncpg/pool.py b/asyncpg/pool.py
index 2e4a7b4f..5c7ea9ca 100644
--- a/asyncpg/pool.py
+++ b/asyncpg/pool.py
@@ -574,7 +574,12 @@ async def _get_new_connection(self):
 
         return con
 
-    async def execute(self, query: str, *args, timeout: float=None) -> str:
+    async def execute(
+        self,
+        query: str,
+        *args,
+        timeout: Optional[float]=None,
+    ) -> str:
         """Execute an SQL command (or commands).
 
         Pool performs this operation using one of its connections.  Other than
@@ -586,7 +591,13 @@ async def execute(self, query: str, *args, timeout: float=None) -> str:
         async with self.acquire() as con:
             return await con.execute(query, *args, timeout=timeout)
 
-    async def executemany(self, command: str, args, *, timeout: float=None):
+    async def executemany(
+        self,
+        command: str,
+        args,
+        *,
+        timeout: Optional[float]=None,
+    ):
         """Execute an SQL *command* for each sequence of arguments in *args*.
 
         Pool performs this operation using one of its connections.  Other than
diff --git a/asyncpg/prepared_stmt.py b/asyncpg/prepared_stmt.py
index d66a5ad3..0c2d335e 100644
--- a/asyncpg/prepared_stmt.py
+++ b/asyncpg/prepared_stmt.py
@@ -6,6 +6,7 @@
 
 
 import json
+import typing
 
 from . import connresource
 from . import cursor
@@ -232,7 +233,7 @@ async def fetchmany(self, args, *, timeout=None):
         )
 
     @connresource.guarded
-    async def executemany(self, args, *, timeout: float=None):
+    async def executemany(self, args, *, timeout: typing.Optional[float]=None):
         """Execute the statement for each sequence of arguments in *args*.
 
         :param args: An iterable containing sequences of arguments.