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We consider the issue of deadline tardiness under global multiprocessor scheduling algorithms. We present a general tardiness-bound derivation that is applicable to a wide variety of such algorithms (including some whose tardiness behavior has not been analyzed before). Our derivation is very general: job priorities may change rather arbitrarily at runtime, capacity restrictions may exist on certain processors, and, under certain conditions, non-preemptive regions are allowed. Our results show that, with the exception of static-priority algorithms, most global algorithms considered previously have bounded tardiness. In addition, our results provide a simple means for checking whether tardiness is bounded under newly-developed algorithms.