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Offset-based response time analysis of tasks scheduled with fixed priorities has demonstrated to be a powerful tool to analyze many task models with different kinds of timing constraints, like regular periodic tasks, suspending tasks, distributed systems, tasks with varying priorities, multi frame models, etc. Offset-based analysis techniques are capable of performing a global schedulability analysis in distributed systems, as opposed to the less efficient techniques that consider each processing or communication resource as independent. In this paper we extend the offset-based schedulability analysis techniques to system with EDF (earliest deadline first) scheduling, using analytical techniques that are similar to those developed for fixed priority scheduling. With this new analysis, we now have a complete set of techniques to perform the analysis of different task models in distributed heterogeneous systems, i.e., processors and communication networks having either fixed priority or EDF schedulers.