Abstract. We introduce a Stochastic Process Algebra called nPEPA, based on Hillston's PEPA. nPEPA is suitable for describing and analysing the performance of certain kinds of queues, such as Ph/Ph/c and M/Ph/1. The activities of nPEPA components have durations given by phase-type distributions. To overcome the state space explosion that arises when solving the models through the underlying Markov process we instead use the Matrix-Geometric Method. Though the method proposed here can only be applied to a fragment of nPEPA because of its dependence on the structure of the system, we can solve models with potentially infinitely many customers queued (an unbounded buffer), in contrast to the approaches used in SPAs such as PEPA, TIPP and EMPA.