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, multiframe 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 systems with EDF 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.