Abstract: In applications ranging from video reception to telecommunications and packet communication to aircraft control, tasks enter periodically and have fixed response time constraints, but missing a deadline is acceptable, provided most deadlines are met. We call such tasks ``occasionally skippable''. We look at the problem of uniprocessor scheduling of occasionally skippable periodic tasks in an environment having periodic tasks. We show that making optimal use of skips is NP-hard. We then look at two algorithms called Skip-Over Algorithms (one a variant of earliest deadline first and one of rate monotonic scheduling) that exploit skips. We give schedulability bounds for both.