diff --git a/httpx/_client.py b/httpx/_client.py
index 13cd933673..22c6a88de6 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
 
@@ -140,13 +141,14 @@ class BoundSyncStream(SyncByteStream):
     """
     A byte stream that is bound to a given response instance, and that
     ensures the `response.elapsed` is set once the response is closed.
+    Uses weakref to avoid reference cycles with the response object.
     """
 
     def __init__(
         self, stream: SyncByteStream, response: Response, start: float
     ) -> None:
         self._stream = stream
-        self._response = response
+        self._response_ref: weakref.ref[Response] = weakref.ref(response)
         self._start = start
 
     def __iter__(self) -> typing.Iterator[bytes]:
@@ -155,7 +157,9 @@ 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_ref()
+        if response is not None:
+            response.elapsed = datetime.timedelta(seconds=elapsed)
         self._stream.close()
 
 
@@ -163,13 +167,14 @@ class BoundAsyncStream(AsyncByteStream):
     """
     An async byte stream that is bound to a given response instance, and that
     ensures the `response.elapsed` is set once the response is closed.
+    Uses weakref to avoid reference cycles with the response object.
     """
 
     def __init__(
         self, stream: AsyncByteStream, response: Response, start: float
     ) -> None:
         self._stream = stream
-        self._response = response
+        self._response_ref: weakref.ref[Response] = weakref.ref(response)
         self._start = start
 
     async def __aiter__(self) -> typing.AsyncIterator[bytes]:
@@ -178,7 +183,9 @@ 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_ref()
+        if response is not None:
+            response.elapsed = datetime.timedelta(seconds=elapsed)
         await self._stream.aclose()
 
 
diff --git a/tests/test_bound_stream.py b/tests/test_bound_stream.py
new file mode 100644
index 0000000000..0422f64225
--- /dev/null
+++ b/tests/test_bound_stream.py
@@ -0,0 +1,100 @@
+"""
+Tests for BoundSyncStream and BoundAsyncStream weakref behavior.
+These tests verify that the streams properly break reference cycles
+to allow garbage collection.
+"""
+
+import gc
+import typing
+import weakref
+
+import pytest
+
+import httpx
+from httpx._client import BoundAsyncStream, BoundSyncStream
+from httpx._types import AsyncByteStream, SyncByteStream
+
+
+class MockSyncStream(SyncByteStream):
+    def __init__(self) -> None:
+        self.closed = False
+
+    def __iter__(self) -> typing.Iterator[bytes]:  # pragma: no cover
+        yield b"test"
+
+    def close(self) -> None:
+        self.closed = True
+
+
+class MockAsyncStream(AsyncByteStream):
+    def __init__(self) -> None:
+        self.closed = False
+
+    async def __aiter__(self) -> typing.AsyncIterator[bytes]:  # pragma: no cover
+        yield b"test"
+
+    async def aclose(self) -> None:
+        self.closed = True
+
+
+def test_bound_sync_stream_sets_elapsed():
+    response = httpx.Response(200, content=b"")
+    stream = MockSyncStream()
+    bound_stream = BoundSyncStream(stream, response=response, start=0.0)
+    bound_stream.close()
+    assert hasattr(response, "_elapsed")
+    assert response.elapsed.total_seconds() >= 0
+
+
+def test_bound_sync_stream_handles_collected_response():
+    response = httpx.Response(200, content=b"")
+    stream = MockSyncStream()
+    bound_stream = BoundSyncStream(stream, response=response, start=0.0)
+    del response
+    gc.collect()
+    bound_stream.close()
+    assert stream.closed
+
+
+def test_bound_sync_stream_no_reference_cycle():
+    response = httpx.Response(200, content=b"")
+    response_ref = weakref.ref(response)
+    stream = MockSyncStream()
+    bound_stream = BoundSyncStream(stream, response=response, start=0.0)
+    response.stream = bound_stream
+    del response
+    gc.collect()
+    assert response_ref() is None, "Response should have been garbage collected"
+
+
+@pytest.mark.anyio
+async def test_bound_async_stream_sets_elapsed():
+    response = httpx.Response(200, content=b"")
+    stream = MockAsyncStream()
+    bound_stream = BoundAsyncStream(stream, response=response, start=0.0)
+    await bound_stream.aclose()
+    assert hasattr(response, "_elapsed")
+    assert response.elapsed.total_seconds() >= 0
+
+
+@pytest.mark.anyio
+async def test_bound_async_stream_handles_collected_response():
+    response = httpx.Response(200, content=b"")
+    stream = MockAsyncStream()
+    bound_stream = BoundAsyncStream(stream, response=response, start=0.0)
+    del response
+    gc.collect()
+    await bound_stream.aclose()
+    assert stream.closed
+
+
+@pytest.mark.anyio
+async def test_bound_async_stream_no_reference_cycle():
+    response = httpx.Response(200, content=b"")
+    response_ref = weakref.ref(response)
+    stream = MockAsyncStream()
+    bound_stream = BoundAsyncStream(stream, response=response, start=0.0)
+    response.stream = bound_stream
+    del response
+    gc.collect()
+    assert response_ref() is None, "Response should have been garbage collected"