Analytical solutions for the mean cycle time of a two-stage series production system with variable operation times at the stages are presented. Although the methodology is applicable to any type of service time distribution at the stages, typical cases of Erlang and normal distributions are worked out in detail. It is shown that the problem of a multi-stage unpaced belt production system can, in principle, be reduced to one of integration, for arbitrary service time distributions at the stages. Detailed expressions are obtained for the mean cycle time and in process inventory of a two-stage series production system with provision for an arbitrary level of interstage inventory. The service time at one of the stages is assumed to be constant and the other distributed exponentially. The analysis leads to the conclusion that at high values of coefficient of variation, the type of service time distribution has a considerable effect on the overall throughput of the system and unbalancing has a favourable effect on the efficiency of a two-stage series system when the variability of service times at the stages is not the same.