An irreversible cycle model is used to investigate the performance of an n-stage combined refrigeration system affected by the irreversibility of finite-rate heat transfer and the internal dissipation of the working fluid. Some reasonable parameters are introduced so that the optimal performance of the irreversible combined refrigeration system may be directly derived by an equivalent simplified cycle model. The optimal relation between the coefficient of performance and the specific cooling load of the system is obtained. The optimal combined conditions between two adjacent irreversible cycles in the system, i.e. the optimal ratios of the temperatures of the working fluids in the heat-transfer processes and the optimal distribution of the heat-transfer areas of the heat exchangers in the system, are determined. The results obtained here are general and useful. They may be used to discuss the optimal performance of an arbitrary-stage irreversible and endoreversible combined refrigeration system. Moreover, it is pointed out that the optimal performance of an arbitrary-stage irreversible and endoreversible combined heat pump system may also be derived from the cycle model.