Recently, a new approach to the symbolic model checking of timed automata based on a partial order semantics was introduced, which relies on event zones that use vectors of event occurrences instead of clock zones that use vectors of clock values grouped in polyhedral clock constraints. Symbolic state exploration with event zones rather than clock zones can result in significant reductions in the number of symbolic states explored. In this work, we show how to extend the event zone approach to networks of automata with local state invariants, an important feature for modeling complex timed systems. To avoid formalizing local states, we attach to each transition an urgency constraint, that allows to code local state invariants. We have integrated the extension into a prototype tool with event zones and reported very promising experimental results.