The behavioral specification of an object-oriented grammar model is considered. The model is based on full lexicalization, head-orientation via valency constraints and dependency relations, inheritance as a means for non-redundant lexicon specification, and concurrency of computation. The computation model relies upon the actor paradigm, with concurrency entering through asynchronous message passing between actors. In particular, we here elaborate on principles of how the global behavior of a lexically distributed grammar and its corresponding parser can be specified in terms of event type networks and event networks, resp.