diff --git a/CHANGELOG.md b/CHANGELOG.md
index 57fa44b8ef..22d0ffd300 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,10 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
 
 ## [UNRELEASED]
 
+### Fixed
+
+* Avoid creating references cycles from `BoundSyncStream` and `BoundAsyncStream` to the response object.  This allows memory to be freed by reference counting, which happens quickly, rather than waiting for the cyclic GC to run.
+
 ### Removed
 
 * Drop support for Python 3.8
diff --git a/httpx/_client.py b/httpx/_client.py
index 13cd933673..c4ae96ddbe 100644
--- a/httpx/_client.py
+++ b/httpx/_client.py
@@ -6,6 +6,7 @@
 import time
 import typing
 import warnings
+import weakref
 from contextlib import asynccontextmanager, contextmanager
 from types import TracebackType
 
@@ -146,7 +147,7 @@ def __init__(
         self, stream: SyncByteStream, response: Response, start: float
     ) -> None:
         self._stream = stream
-        self._response = response
+        self._response = weakref.ref(response)
         self._start = start
 
     def __iter__(self) -> typing.Iterator[bytes]:
@@ -155,7 +156,9 @@ def __iter__(self) -> typing.Iterator[bytes]:
 
     def close(self) -> None:
         elapsed = time.perf_counter() - self._start
-        self._response.elapsed = datetime.timedelta(seconds=elapsed)
+        response = self._response()
+        if response is not None:
+            response.elapsed = datetime.timedelta(seconds=elapsed)
         self._stream.close()
 
 
@@ -169,7 +172,7 @@ def __init__(
         self, stream: AsyncByteStream, response: Response, start: float
     ) -> None:
         self._stream = stream
-        self._response = response
+        self._response = weakref.ref(response)
         self._start = start
 
     async def __aiter__(self) -> typing.AsyncIterator[bytes]:
@@ -178,7 +181,9 @@ async def __aiter__(self) -> typing.AsyncIterator[bytes]:
 
     async def aclose(self) -> None:
         elapsed = time.perf_counter() - self._start
-        self._response.elapsed = datetime.timedelta(seconds=elapsed)
+        response = self._response()
+        if response is not None:
+            response.elapsed = datetime.timedelta(seconds=elapsed)
         await self._stream.aclose()