Each processor in a uniform multiprocessor machine is characterized by a speed or computing capacity, with the interpretation that a job executing on a processor with speed s for t time units completes (s /spl times/ t) units of execution. The earliest deadline first (EDF) scheduling of hard-real-time systems upon uniform multiprocessor machines is considered. It is known that online algorithms tend to perform very poorly in scheduling such hard-real-time systems on multiprocessors; resource-augmentation techniques are presented here that permit online algorithms in general (EDF in particular) to perform better than may be expected given these inherent limitations. It is shown that EDF scheduling upon uniform multiprocessors is robust with respect to both job execution requirements and processor computing capacity.