Prior work on Pfair scheduling has resulted in three optimal multiprocessor scheduling algorithms, and one algorithm, EPDF, that is less expensive but not optimal. EPDF is still of interest in soft real-time systems, however, due to its ability to guarantee bounded tardiness. In particular, it has been shown that a tardiness bound of t quanta is possible under EPDF if all task weights (i.e., shares or utilizations) are restricted to a value specified as a function of t. In an actual system, however, different tasks may be subject to different tardiness bounds. If such a system is scheduled under EPDF, then the tardiness of a task with a higher bound may cause the tardiness bound of a task with a lower bound to be violated; that is, temporal isolation among the various tardiness classes may not be guaranteed. In this paper, we propose an algortihm based on EPDF for scheduling task classes with different tardiness bounds on a multiprocessor. Our algorithm provides temporal isolation among classes, allows the available processing capacity to be fully utilized, and does not require that previously established per-task weight restrictions be made more stringent.