Recently we have presented distributed dynamic condition response structures (DCR structures) as a declarative process model conservatively generalizing labelled event structures to allow for finite specifications of repeated, possibly infinite behavior. The key ideas are to split the causality relation of event structures in two dual relations: the condition relation and the response relation, to split the conflict relation in two relations: the dynamic exclusion and dynamic inclusion, and finally to allow configurations to be multi sets of events. In the present abstract we recall the model and show how to characterise the execution of DCR structures and the acceptance condition for infinite runs by giving a map to Bu ̈chi-automata. This is the first step towards automatic verification of processes specified as DCR structures.