diff --git a/src/mcp/client/session_group.py b/src/mcp/client/session_group.py
index 961021264..d900789bd 100644
--- a/src/mcp/client/session_group.py
+++ b/src/mcp/client/session_group.py
@@ -13,7 +13,6 @@
 from types import TracebackType
 from typing import Any, TypeAlias
 
-import anyio
 import httpx
 from pydantic import BaseModel, Field
 from typing_extensions import Self
@@ -165,10 +164,9 @@ async def __aexit__(
         if self._owns_exit_stack:
             await self._exit_stack.aclose()
 
-        # Concurrently close session stacks.
-        async with anyio.create_task_group() as tg:
-            for exit_stack in self._session_exit_stacks.values():
-                tg.start_soon(exit_stack.aclose)
+        # Sequentially close session stacks to preserve AnyIO task contexts.
+        for exit_stack in list(self._session_exit_stacks.values()):
+            await exit_stack.aclose()
 
     @property
     def sessions(self) -> list[mcp.ClientSession]:
diff --git a/tests/client/test_session_group.py b/tests/client/test_session_group.py
index 6a58b39f3..ad46f4af0 100644
--- a/tests/client/test_session_group.py
+++ b/tests/client/test_session_group.py
@@ -1,9 +1,17 @@
 import contextlib
+import socket
+import sys
+from typing import cast
 from unittest import mock
 
 import httpx
 import pytest
 
+if sys.version_info >= (3, 11):
+    from builtins import BaseExceptionGroup, ExceptionGroup
+else:
+    from exceptiongroup import BaseExceptionGroup, ExceptionGroup
+
 import mcp
 from mcp import types
 from mcp.client.session_group import (
@@ -385,3 +393,113 @@ async def test_client_session_group_establish_session_parameterized(
             # 3. Assert returned values
             assert returned_server_info is mock_initialize_result.server_info
             assert returned_session is mock_entered_session
+
+
+def _free_tcp_port() -> int:
+    """Return a TCP port number not currently bound on localhost."""
+    with socket.socket(socket.AF_INET, socket.SOCK_STREAM) as sock:
+        sock.bind(("127.0.0.1", 0))
+        return sock.getsockname()[1]
+
+
+def _is_cancel_scope_runtime_error(exc: BaseException | None) -> bool:
+    """Walk an exception chain looking for AnyIO cancel-scope RuntimeError."""
+    seen: set[int] = set()
+
+    def _walk(current: BaseException | None) -> bool:
+        if current is None or id(current) in seen:
+            return False
+        seen.add(id(current))
+
+        if isinstance(current, RuntimeError) and "cancel scope" in str(current).lower():
+            return True
+        if isinstance(current, BaseExceptionGroup):
+            group = cast("BaseExceptionGroup[BaseException]", current)
+            return any(_walk(child) for child in group.exceptions)
+        return _walk(current.__cause__) or _walk(current.__context__)
+
+    return _walk(exc)
+
+
+@pytest.mark.anyio
+async def test_unreachable_streamable_http_error_is_catchable() -> None:
+    """Unreachable streamable-http servers raise catchable connection errors."""
+    port = _free_tcp_port()
+    server_params = StreamableHttpParameters(url=f"http://127.0.0.1:{port}/mcp/")
+
+    caught: BaseException | None = None
+
+    try:
+        async with ClientSessionGroup() as group:
+            try:
+                await group.connect_to_server(server_params)
+            except BaseException as inner:  # noqa: BLE001
+                caught = inner
+    except BaseException as outer:  # noqa: BLE001
+        caught = outer
+
+    assert caught is not None, (
+        "Expected to catch a connection error against an unreachable "
+        "streamable-http server, but no exception was raised."
+    )
+    assert not _is_cancel_scope_runtime_error(caught), (
+        "Regression of #915: connection error against an unreachable "
+        "streamable-http server was masked by an anyio cancel-scope "
+        f"RuntimeError. Got: {type(caught).__name__}: {caught}"
+    )
+
+
+def test_is_cancel_scope_runtime_error_detected() -> None:
+    exc = RuntimeError("Attempted to exit cancel scope in a different task")
+
+    assert _is_cancel_scope_runtime_error(exc)
+
+
+def test_is_cancel_scope_runtime_error_in_group_detected() -> None:
+    exc = ExceptionGroup(
+        "outer",
+        [ValueError("other"), RuntimeError("Attempted to exit cancel scope in a different task")],
+    )
+
+    assert _is_cancel_scope_runtime_error(exc)
+
+
+def test_is_cancel_scope_non_runtime_error_not_detected() -> None:
+    assert not _is_cancel_scope_runtime_error(ValueError("cancel scope was mentioned"))
+
+
+def test_is_cancel_scope_none_is_false() -> None:
+    assert not _is_cancel_scope_runtime_error(None)
+
+
+def test_is_cancel_scope_in_cause_chain() -> None:
+    exc = ValueError("outer")
+    exc.__cause__ = RuntimeError("Attempted to exit cancel scope in a different task")
+
+    assert _is_cancel_scope_runtime_error(exc)
+
+
+@pytest.mark.anyio
+async def test_session_group_with_external_exit_stack(
+    mock_exit_stack: mock.MagicMock,
+) -> None:
+    """External exit stacks remain caller-managed."""
+    group = ClientSessionGroup(exit_stack=mock_exit_stack)
+
+    async with group:
+        pass
+
+    mock_exit_stack.__aenter__.assert_not_called()
+    mock_exit_stack.aclose.assert_not_called()
+
+
+@pytest.mark.anyio
+async def test_session_group_teardown_closes_session_stacks() -> None:
+    """__aexit__ closes every session-level exit stack sequentially."""
+    session = mock.MagicMock(spec=mcp.ClientSession)
+    session_stack = mock.AsyncMock()
+
+    async with ClientSessionGroup() as group:
+        group._session_exit_stacks[session] = session_stack
+
+    session_stack.aclose.assert_awaited_once()