I think the issue is that search engines will see hxxp://www.****** and hxxp://****** as 2 distinct entities, but both showing the same content.
There are 2 things you can do:
1) Modify your .htaccess file to route traffic to one or the other, the most common way of doing this is rewriting non-www urls to www.
2) Specify your canonical URL. Basically if you can retrieve the same content via 2 or more URLs, then you should specify which the search engines should take as being, essentially, the primary URL and therefore ignore the others. Have a read here: googlewebmastercentral.blogspot.com/2009/02/specify-your-canonical.html