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Hybrid Rebeca is a modeling framework for asynchronous event-based cyber–physical systems (CPSs). In this work, we extend Hybrid Rebeca to allow the modeling of non-deterministic time behaviour. Besides the syntactical extension, we formalize the semantics of the extended language in terms of Timed Transition Systems, and adapt a reachability analysis algorithm originally designed for hybrid automata to be applicable to Hybrid Rebeca models. We prove the soundness of our approach and illustrate its applicability on two examples: a thermostat with alarm and a simplified brake-by-wire system with anti-lock braking system. We demonstrate that our dedicated algorithm is clearly superior to the alternative approach of transforming Hybrid Rebeca models to hybrid automata as an intermediate model and then applying the original reachability analysis method to these intermediate transformed models.