A combined cycle model which includes the irreversibilities of finite-rate heat transfer in heat-exchange processes and heat leak loss of the heat source is used to analyse the performance of a multi-stage Carnot heat engine system. The efficiency, power output, ecological function and profit of operating the combined system are optimized. The optimally operating region of the combined system is determined. The optimal combined conditions between two adjacent cycles in the combined system are obtained. Moreover, the cycle model is generalized to include the internal irreversibilities of the working fluids so that the results obtained here become more general. Copyright (C) 2001 John Wiley & Sons, Ltd.