A cascade endo-reversible heat-pump system was modelled, and is described on the basis of a single-stage endo-reversible heat-pump. A performance analysis of the system was carried out, and the specific heating load of the system was optimised for a given coefficient of performance. General performance characteristic curves of the system were obtained. In this paper the optimal combination between two adjacent cycles in the cascade system is discussed. The optimal ratios of the temperatures of the working fluids in the heat-transfer processes were determined, and the optimal distribution of the heat-transfer areas of the heat-exchangers in the cascade system was proven to be the same as that of the heat-transfer areas of the heat-exchangers in the multi-stage endo-reversible refrigeration systems.