301 redirects is used when url of the page is changed permanently. For e.g. you have one domain named www.abc.com with good SEO ranking and now you want to change www.abc.com to www.xyz.com then 301 redirects should be used on old url here www.abc.com.

But what is your problem is that search engine is indexing your domain in two version. one is with www and another is without www.

if you want to control this indexing in google then you need to set your preferred domain in google webmaster tool. Under site configuration in google webmaster there is settings option. Under this you can set your preferred domain. I have no idea about other search engine. If you find any difficulty in google webmaster then revert back here.

---

Thanks & Regards,
Nandip Makwana
DotnetExpertGuide