The following technical report is available from http://aib.informatik.rwth-aachen.de: Languages of Infinite Traces and Deterministic Asynchronous Automata Namit Chaturvedi AIB 2014-04 In the theory of deterministic automata for languages of infinite words, a fundamental fact relates the family of infinitary limits of regular languages and the family of omega-languages recognized by deterministic Buechi automata. With the known definitions of asynchronous automata, this observation does not extend to the context of traces. A major difficulty is posed by processes that stall after finitely many transitions. We introduce the family of deterministic, synchronization-aware asynchronous automata which -- using as parameter the set of processes that stay live ad infinitum -- allows us to settle an open question, namely, whether there exists a deterministic Buechi automaton recognizing precisely the infinitary limit of a regular trace language. Also, the corresponding class of unparameterized Muller automata captures all omega-Regular trace languages.