The problem of scheduling multiple streams of real-time customers is addressed in this paper. The paper rst introduces the notion of (m; k)-rm deadlines to better characterize the timing constraints of real-time streams. More speciically, a stream is said to have (m; k)-rm deadlines if at least m out of any k consecutive customers must meet their deadlines. Note that, the notion of (m; k)-rm deadlines is a generalization of rm and soft deadlines. In particular, m = k = 1 characterizes a stream with rm deadlines. A large value for k with (k ? m)=k equal to the maximum allowable loss rate can be used to represent a stream with soft deadlines. A stream with (m; k)-rm deadlines will experience a dynamic failure if fewer than m out of any k consecutive customers meet their deadlines. The paper proposes a policy for scheduling N such streams on a single server to reduce the probability of dynamic failure. The basic idea of the proposed policy is to assign higher priorities to customers from streams which have had too many recent missed deadlines. The paper proposes a heuristic for assigning these priorities. The eeectiveness of this approach is evaluated through simulation under various customer arrival and service patterns. The evaluation shows that by properly assigning the priorities one can substantially reduce the probability of dynamic failure.