The non-renewal departure processes from a finite capacityG/M/1queueing system (with a non-renewal input, generally distributed interarrival time, a single server, first come first served queueing discipline, and a markovian server) and an M/G/1/K queueing system (with a Poisson input, generally distributed service times, a single server, and first come first served queueing discipline) are approximated by compatible renewal processes, in steady state. Furthermore, numerical results arc provided, and the approximation outcomes are compared against those from a simulation study.