diff --git a/compute_endpoint/globus_compute_endpoint/exception_handling.py b/compute_endpoint/globus_compute_endpoint/exception_handling.py
index 3c848a640..f88ec2e0a 100644
--- a/compute_endpoint/globus_compute_endpoint/exception_handling.py
+++ b/compute_endpoint/globus_compute_endpoint/exception_handling.py
@@ -10,6 +10,7 @@
 from __future__ import annotations
 
 import functools
+import json
 import logging
 import os
 import sys
@@ -86,6 +87,23 @@ def wrapper(*args, **kwargs):
                 message:           {e.text}
                 """
             )
+
+            # This specific Auth error has a common cause
+            if e.http_status == 400 and e.code == "Error":
+                try:
+                    error_info = json.loads(e.text)
+                    if "invalid_grant" == error_info.get("error"):
+                        msg += (
+                            "\nGlobus Compute credentials may have expired."
+                            " Use `logout` to clear them.\n"
+                            "Note that Globus Connect (Transfer) credentials are"
+                            " managed via the `globus` command, separately from"
+                            " the Globus Compute ones."
+                        )
+                except Exception:
+                    # Shouldn't get here unless Globus Auth changes its response
+                    pass
+
             log.warning(msg)
             click.echo(msg)
             sys.exit(os.EX_NOPERM)
diff --git a/compute_endpoint/tests/unit/test_cli_behavior.py b/compute_endpoint/tests/unit/test_cli_behavior.py
index 1515c6407..a8e951b80 100644
--- a/compute_endpoint/tests/unit/test_cli_behavior.py
+++ b/compute_endpoint/tests/unit/test_cli_behavior.py
@@ -666,9 +666,11 @@ def test_get_endpoint_by_name_or_uuid_error_message(run_line, data):
 @pytest.mark.parametrize(
     "data",
     [
-        ("start", "start_endpoint"),
-        ("stop", "stop_endpoint"),
-        ("delete --yes", "delete_endpoint"),
+        ("start", "start_endpoint", '{"error":"invalid_grant"}'),
+        ("start", "start_endpoint", '{"error":"something else"}'),
+        ("start", "start_endpoint", ""),
+        ("stop", "stop_endpoint", "err_msg"),
+        ("delete --yes", "delete_endpoint", "err_msg"),
     ],
 )
 def test_handle_globus_auth_error(
@@ -679,15 +681,20 @@ def test_handle_globus_auth_error(
     ep_name,
     data: tuple[str, str],
 ):
-    cmd, ep_method = data
+    cmd, ep_method, auth_err_msg = data
     mock_ep, _ = mock_cli_state
     make_endpoint_dir()
 
     mock_log = mocker.patch("globus_compute_endpoint.exception_handling.log")
+    mock_resp = mock.MagicMock(
+        status_code=400,
+        reason="Bad Request",
+        text=auth_err_msg,
+    )
     mocker.patch.object(
         mock_ep,
         ep_method,
-        side_effect=globus_sdk.AuthAPIError(r=mock.MagicMock(status_code=400)),
+        side_effect=globus_sdk.AuthAPIError(r=mock_resp),
     )
 
     res = run_line(f"{cmd} {ep_name}", assert_exit_code=os.EX_NOPERM)
@@ -699,3 +706,9 @@ def test_handle_globus_auth_error(
     assert err_msg in a[0]
     assert "400" in res.stdout
     assert "400" in a[0]
+
+    additional_details = "credentials may have expired"
+    if "invalid_grant" in auth_err_msg:
+        assert additional_details in res.stdout
+    else:
+        assert additional_details not in res.stdout