This paper considers the scheduling of soft real-time sporadic task systems under global EDF on an identical multiprocessor. Prior research on global EDF has focussed mostly on hard real-time systems, where, to ensure that all deadlines are met, approximately 50% of the available processing capacity will have to be sacrificed in the worst case. This may be overkill for soft real-time systems that can tolerate bounded tardiness. In this paper, we derive tardiness bounds under preemptive and non-preemptive global EDF on multiprocessors when the total utilization of a task system is not restricted and may equal the number of processors. Our tardiness bounds depend on per-task utilizations and execution costs — the lower these values, the lower the tardiness bounds. As a final remark, we note that global EDF may be superior to partitioned EDF for multiprocessor-based soft real-time systems in that the latter does not offer any scope to improve system utilization even if bounded tardiness can be tolerated.