This paper investigates an ATM multiplexer with a resume level, which uses a selective cell discarding strategy as a priority control, and a Markov-modulated deterministic process (MMDP) as the burst input traffic. Assuming that a system is loaded with a superposition of several independent and homogeneous On-Off bursty sources with two priority classes, we obtain the cell loss probability of each priority class of an ATM multiplexer with a resume level. The performance analysis derived here includes as special cases one without priority and one with a threshold level. From the numerical results, we compare the cell loss probability, the mean queue length, the mean queuing delay, the level crossing rate, and the queue length distribution at the embedded points for the case of a threshold level with those for the case of a resume level. By selecting an appropriate resume level, we can reduce the sensitive state change around the threshold level.