The authors consider an M/G/1 priority retrial queueing system with two types of calls which models a telephone switching system and a cellular mobile communication system. In the case that arriving calls are blocked due to the server being busy, type I calls the queued in a priority queue of finite capacity K whereas type II calls enter the retrial group in order to try service again after a random amount of time. In this paper the authors find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form. When λ1=0, it is shown that the present results are consistent with the known results for a classical retrial queueing system.
