Will permanent redirects update the urls in the SE indexes?

[Grinler]

I am using rewriting some apps on my site and unfortunately the urls to the various pages in this app are going to change. I will use rewrite rules so that people will still be able to get to them, but am wondering how I can have the Search Engines use the new url.

Can i redirect using a permanent redirect and when a search engine visits, will see that permanent (301) redirect and update the url in the index? My concern is that i keep reading that 302 may cause problems with SEs...is that the case with 301 redirects as well or are those considered legit?