Unfortunately this could be the result of any number of things, from a problem with your hardware that Win ME is exposing, to a bad install, to slightly incompatible drivers, to little green blobby things from Alpha Centuri invading your computer in a mad plot to destroy the world.
The first thing to ask, of course, is if this problem manifests itself outside of UnrealTournament. If not, then perhaps it's time to start eliminating potential sources of error by freshly reinstalling first UT, then hardware drivers, and if need be, Windows ME.