I have no idea what doubletrader is but yes you can put CJ and Adsense on same page. What you can't put are Yahoo and Google contextual ads on same page, for example.

Sorry I meant tradedoubler. So contextual based ads are bits of code like adsense right? I mean I could put a text link on my page with an affiliate ID on it right? Like a static link? I'm also assuming banners make no difference?

It has nothing to do with the code, it has to do with targeted ads (context).

For example, if you're running Adsense, then you cannot run another program on that same page that reads what is on the page and serves up advertisements based on that page's content (the way that Adsense does).

you can run tradedoubler because is not contextual