A cycle model of a multi-stage combined heat pump system, which includes the irreversibility of finite rate heat transfer across finite temperature differences and the irreversibilities inside the working fluid, is established and used to investigate the influence of these irreversibilities on the performance of the system. The profit of operating the heat pump system is taken as an objective function for optimization. The maximum profit is calculated for a given total heat transfer area or total thermal conductance of heat exchangers. The coefficient of performance, heating load, and power input at the maximum profit are determined. The distribution of the heat transfer areas or the thermal conductances of heat exchangers and the temperature ratios of the working fluids of two adjacent cycles in heat exchange processes are optimized. The results obtained here are generally significant. They are suitable for an arbitrary-stage irreversible and endoreversible combined heat pump system. [S0195-0738(00)01104-3].