Yes, you will need to convert them. If you have QuickTime Pro, you can open the files in it and then convert them to whatever format you wish.
If not, you can download the free MPEG-Streamclip and try it: http://www.squared5.com/svideo/mpeg-streamclip-mac.html
Open it, drag the .asf clip to it and convert.
I could not find out from their website whether Streamclip can convert .asf files, but a search in these discussions produced these threads where it is recommended, and some other info that might be helpful to you:
http://discussions.apple.com/thread.jspa?threadID=2282788
http://discussions.apple.com/thread.jspa?threadID=1625544
http://discussions.apple.com/thread.jspa?threadID=1588020
And these:
http://forums.macworld.com/index.php?/topic/91455-how-to-get-asf-into-imovie/
http://www.mp4kits.com/Guides/iMovie/import-asf-to-imovie/
Good luck...Hope one of these can help you get your movies into iMovie.
If not, you can download the free MPEG-Streamclip and try it: http://www.squared5.com/svideo/mpeg-streamclip-mac.html
Open it, drag the .asf clip to it and convert.
I could not find out from their website whether Streamclip can convert .asf files, but a search in these discussions produced these threads where it is recommended, and some other info that might be helpful to you:
http://discussions.apple.com/thread.jspa?threadID=2282788
http://discussions.apple.com/thread.jspa?threadID=1625544
http://discussions.apple.com/thread.jspa?threadID=1588020
And these:
http://forums.macworld.com/index.php?/topic/91455-how-to-get-asf-into-imovie/
http://www.mp4kits.com/Guides/iMovie/import-asf-to-imovie/
Good luck...Hope one of these can help you get your movies into iMovie.