M4P files are typically DRM-protected songs purchased from iTunes when they still did that sort of thing. (Now they sell exclusively unprotected M4A files.) If that's the case with you, then you can do one of two things for those songs:
- For songs that are still available on iTunes, they will allow you to pay some money (I think 30 cents per song) to give you access to the unprotected version of the same file. Start up iTunes and see if "iTunes Plus" appears in the right-hand margin. If it's there, click on it, and it will show you which songs are eligible for an upgrade. Once you have the M4A file, and you're pointing your Zune music library to the directory your iTunes downloads end up in, you should be able to play the file just fine.
- You can burn the M4P files to an audio CD, and then rip the CD back into either M4A or MP3. The resulting files will be unprotected and work properly in Zune.