A heuristic algorithm is suggested for approximating the departure process from a G/M/1 queueing system with generally distributed interarrival times, a single markovian server, an infinite capacity, and the first-come first-served queueing discipline, in the steady state. The tandem behaviour of the system is then approximated in the steady state. Finally, the approximation results are compared against both a simulation study and the approximation results of Kuehn (1979) and Whitt (1983 a, b).