diff --git a/src/mcp/client/sse.py b/src/mcp/client/sse.py
index 0c05c6def..4541935a7 100644
--- a/src/mcp/client/sse.py
+++ b/src/mcp/client/sse.py
@@ -51,8 +51,8 @@ async def sse_client(
     read_stream_writer, read_stream = anyio.create_memory_object_stream(0)
     write_stream, write_stream_reader = anyio.create_memory_object_stream(0)
 
-    async with anyio.create_task_group() as tg:
-        try:
+    try:
+        async with anyio.create_task_group() as tg:
             logger.debug(f"Connecting to SSE endpoint: {remove_request_params(url)}")
             async with httpx_client_factory(
                 headers=headers, auth=auth, timeout=httpx.Timeout(timeout, read=sse_read_timeout)
@@ -139,6 +139,14 @@ async def post_writer(endpoint_url: str):
                         yield read_stream, write_stream
                     finally:
                         tg.cancel_scope.cancel()
-        finally:
-            await read_stream_writer.aclose()
-            await write_stream.aclose()
+    except Exception as e:
+        logger.error(f"TaskGroup exception in SSE transport: {e}")
+        try:
+            await read_stream_writer.send(e)
+        except Exception:
+            logger.error(f"Failed to send TaskGroup exception to read stream: {e}")
+        raise
+
+    finally:
+        await read_stream_writer.aclose()
+        await write_stream.aclose()
diff --git a/src/mcp/client/streamable_http.py b/src/mcp/client/streamable_http.py
index 39ac34d8a..aa48232d5 100644
--- a/src/mcp/client/streamable_http.py
+++ b/src/mcp/client/streamable_http.py
@@ -471,8 +471,8 @@ async def streamablehttp_client(
     read_stream_writer, read_stream = anyio.create_memory_object_stream[SessionMessage | Exception](0)
     write_stream, write_stream_reader = anyio.create_memory_object_stream[SessionMessage](0)
 
-    async with anyio.create_task_group() as tg:
-        try:
+    try:
+        async with anyio.create_task_group() as tg:
             logger.debug(f"Connecting to StreamableHTTP endpoint: {url}")
 
             async with httpx_client_factory(
@@ -504,6 +504,13 @@ def start_get_stream() -> None:
                     if transport.session_id and terminate_on_close:
                         await transport.terminate_session(client)
                     tg.cancel_scope.cancel()
-        finally:
-            await read_stream_writer.aclose()
-            await write_stream.aclose()
+    except Exception as e:
+        logger.error(f"TaskGroup exception in StreamableHTTP transport: {e}")
+        try:
+            await read_stream_writer.send(e)
+        except Exception:
+            logger.error(f"Failed to send TaskGroup exception to read stream: {e}")
+        raise
+    finally:
+        await read_stream_writer.aclose()
+        await write_stream.aclose()