Stopping an "onEnterFrame"

Hi there.
I am developing a flash movie with a series of smooth fade in/out applied to several movie clips.
I want to use AS rather than tweening to do this.
I am using something like “MyClip.onEnterFrame” to realize the animations.
Everything looks and works fine except that it seems the animation becomes an endless loop(the alpha of each movie keeps assuming undefined values) and the whole movie is suffering from it. (The CPU keeps processing i guess).
I’d like to know if there is a way that i can “stop” this loop from happening.
If someone could help please…