Every time I try to run Premiere Elements 10 on my MacBook Pro with OS X Lion it crashes. There is really nothing more to tell. I does not give me an error besides Premiere Elements 10 quit unexpectedly with options to Ignore, Report, or Reopen. I've tried deleting the prefs files and uninstalling and reinstalling with no success. Any other ideas would be welcome. Well, except for creating a new user account. I had problems with PSE a couple of months ago and the solution was to create a new user account. What a PITB! I'm still not completely recovered from that and some things from my old account would not move to my new account at all and were lost. I will not go through that again. If that is the solution, I'll just go back to iMovie and forget PRE.
Depending on the type of video you're using as your source and the depth of editing you're trying to do, iMovie may be your best solution, Carlsoc.
Meantime, do you have any other Adobe programs -- or have you had any other Adobe programs -- installed on your computer? There are known conflicts with with some Creative Suite software.