diff --git a/tests/integration/test_httpbin.py b/tests/integration/test_httpbin.py
index 422f7e2..53da40e 100644
--- a/tests/integration/test_httpbin.py
+++ b/tests/integration/test_httpbin.py
@@ -11,6 +11,9 @@
 
 pytestmark = pytest.mark.integration
 
+# Go reports a timeout as "Client.Timeout exceeded" or "context deadline exceeded", depending on where it hits.
+TIMEOUT = "Timeout exceeded|deadline exceeded"
+
 
 @pytest.fixture
 def session() -> Iterator[Session]:
@@ -241,14 +244,14 @@ def test_refused_connection_raises(self, session):
     def test_session_timeout_raises(self, httpbin, session):
         session.timeout_seconds = 1
 
-        with pytest.raises(TLSClientException, match="Timeout exceeded"):
+        with pytest.raises(TLSClientException, match=TIMEOUT):
             session.get(f"{httpbin.url}/delay/2")
 
     @pytest.mark.parametrize("kwarg", ["timeout", "timeout_seconds"])
     def test_request_timeout_applies_after_the_first_request(self, httpbin, session, kwarg):
         session.get(f"{httpbin.url}/get")
 
-        with pytest.raises(TLSClientException, match="Timeout exceeded"):
+        with pytest.raises(TLSClientException, match=TIMEOUT):
             session.get(f"{httpbin.url}/delay/2", **{kwarg: 1})
 
 
diff --git a/tests/integration/test_local_server.py b/tests/integration/test_local_server.py
index ca23c69..a6d9dcf 100644
--- a/tests/integration/test_local_server.py
+++ b/tests/integration/test_local_server.py
@@ -24,6 +24,8 @@
 LARGE = os.urandom(8 * 1024 * 1024)
 # How long /slow takes to answer.
 SLOW_SECONDS = 0.6
+# Go reports a timeout as "Client.Timeout exceeded" or "context deadline exceeded", depending on where it hits.
+TIMEOUT = "Timeout exceeded|deadline exceeded"
 
 # Path -> (Content-Type, body)
 BODIES = {
@@ -166,7 +168,7 @@ def test_content_type_from_the_session_or_the_request_is_kept(self, server_url,
 class TestTimeout:
     @pytest.mark.parametrize("kwarg", ["timeout", "timeout_seconds"])
     def test_fractional_timeout_is_applied(self, server_url, session, kwarg):
-        with pytest.raises(TLSClientException, match="Timeout exceeded"):
+        with pytest.raises(TLSClientException, match=TIMEOUT):
             session.get(f"{server_url}/slow", **{kwarg: SLOW_SECONDS / 3})
 
     def test_response_within_the_timeout_arrives(self, server_url, session):
@@ -175,7 +177,7 @@ def test_response_within_the_timeout_arrives(self, server_url, session):
     def test_fractional_session_timeout_is_applied(self, server_url, session):
         session.timeout_seconds = SLOW_SECONDS / 3
 
-        with pytest.raises(TLSClientException, match="Timeout exceeded"):
+        with pytest.raises(TLSClientException, match=TIMEOUT):
             session.get(f"{server_url}/slow")