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In work on multiprocessor real-time systems, task scheduling with self-suspensions is a relatively unexplored topic. In this paper, soft real-time sporadic task systems are considered that include self-suspending tasks. Conditions are presented for guaranteeing bounded deadline tardiness in such systems under global EDF or FIFO multiprocessor scheduling. These conditions enable many soft real-time task systems with self-suspending tasks to be scheduled with little or no utilization loss.