diff --git a/httpx/_client.py b/httpx/_client.py
index 13cd933673..763f6577e2 100644
--- a/httpx/_client.py
+++ b/httpx/_client.py
@@ -985,13 +985,18 @@ def _send_handling_redirects(
                 if not response.has_redirect_location:
                     return response
 
-                request = self._build_redirect_request(request, response)
+                try:
+                    next_request = self._build_redirect_request(request, response)
+                except (InvalidURL, RemoteProtocolError):
+                    return response
+
                 history = history + [response]
 
                 if follow_redirects:
                     response.read()
+                    request = next_request
                 else:
-                    response.next_request = request
+                    response.next_request = next_request
                     return response
 
             except BaseException as exc:
@@ -1701,13 +1706,18 @@ async def _send_handling_redirects(
                 if not response.has_redirect_location:
                     return response
 
-                request = self._build_redirect_request(request, response)
+                try:
+                    next_request = self._build_redirect_request(request, response)
+                except (InvalidURL, RemoteProtocolError):
+                    return response
+
                 history = history + [response]
 
                 if follow_redirects:
                     await response.aread()
+                    request = next_request
                 else:
-                    response.next_request = request
+                    response.next_request = next_request
                     return response
 
             except BaseException as exc:
diff --git a/tests/client/test_redirects.py b/tests/client/test_redirects.py
index f65827134c..5150e17114 100644
--- a/tests/client/test_redirects.py
+++ b/tests/client/test_redirects.py
@@ -202,8 +202,11 @@ def test_malformed_redirect():
 
 def test_invalid_redirect():
     client = httpx.Client(transport=httpx.MockTransport(redirects))
-    with pytest.raises(httpx.RemoteProtocolError):
-        client.get("http://example.org/invalid_redirect", follow_redirects=True)
+    response = client.get("http://example.org/invalid_redirect", follow_redirects=True)
+    assert response.status_code == httpx.codes.SEE_OTHER
+    assert response.url == "http://example.org/invalid_redirect"
+    assert not response.history
+    assert response.next_request is None
 
 
 def test_no_scheme_redirect():
@@ -441,7 +444,10 @@ def test_redirect_custom_scheme():
 @pytest.mark.anyio
 async def test_async_invalid_redirect():
     async with httpx.AsyncClient(transport=httpx.MockTransport(redirects)) as client:
-        with pytest.raises(httpx.RemoteProtocolError):
-            await client.get(
-                "http://example.org/invalid_redirect", follow_redirects=True
-            )
+        response = await client.get(
+            "http://example.org/invalid_redirect", follow_redirects=True
+        )
+        assert response.status_code == httpx.codes.SEE_OTHER
+        assert response.url == "http://example.org/invalid_redirect"
+        assert not response.history
+        assert response.next_request is None