I see here two scenarios based on how API which you call works.
First one is definitely easier to handle - calling new credentials (e.g. access token) doesn't expire old one. To achieve it you can add an extra flag to your credentials to say that credentials are being refreshed. When you got 401 response, you set flag to true, make a request to get new credentials and you save them only if flag equals true so only first response will be handled and rest of them will be ignored. Make sure that your access to flag is synchronized.
Another scenario is a little bit more tricky - every time when you call new credentials old one are set to be expired by server side. To handle it you I would introduce new object to be used as a semafore - it would be blocked every time when 'credentials are being refreshed'. To make sure that you'll make only one 'refresh credentials' call, you need to call it in block of code which is synchronized with flag. It can look like it:
synchronized(stateObject) {
if(!stateObject.isBeingRefreshed) return;
Response response = client.execute(request);
apiClient.setCredentials(response.getNewCredentials());
stateObject.isBeingRefreshed = false;
}
As you've noticed there is an extra check if(!stateObject.isBeingRefreshed) return;
to cancel requesting new credentials by following requests which received 401 response.