Introduction:
It’s not easy to debug ajax applications.Reason was “THE BROWSER REQUEST AND SERVER RESPONSE OCCUR IN BACKGROUND.In Market some of the tools are available for troubleshooting AJAX applications.

Main:

Some of the Important tools are,

1.Firebug Console –> Simply,the Firebug console logs the XMLHttpRequest, and you can view both the response and the headers in the console.

2.Live HTTP Headers –> Is a Firefox extension that shows HTTP Headers in real time and enables you to track HTTP requests and responses. You can be downloaded at http://www.livehttpheaders.mozdev.org/.

3.ieHTTPHeaders Explorer Bar –>  IeHTTPHeaders Explorer Bar is a free toolbar for IE that displays HTTP headers in real time.Just you need to activate HTTPHeader after Installation Toolbars ? Explorer Bar ? ieHTTPHeaders.You can be downloaded at http://www.blunck.info/iehttpheaders.html.

Conclusion:
These are very useful some complex ajax applications.
Hope,this helps,
Happy Coding.