  In this paper we consider the problem of proving properties of infinite
behaviour of formalisms suitable to describe (infinite state) systems with
recursion and parallelism. As a formal setting, we consider the framework of
Process Rewriting Systems (PRSs). For a meaningfull fragment of PRSs, allowing
to accommodate both Pushdown Automata and Petri Nets, we state decidability
results for a class of properties about infinite derivations (infinite term
rewritings). The given results can be exploited for the automatic verification
of some classes of linear time properties of infinite state systems described
by PRSs. In order to exemplify the assessed results, we introduce a meaningful
automaton based formalism which allows to express both recursion and
multi--treading.
