The effects of thermal resistances and internal irreversibilities on the performance of combined cycles (combined four stage vapour compression cycles and solar driven combined Brayton power and refrigeration cycles) for cryogenic refrigeration were investigated. Improved equations for the coefficient of performance of the systems under consideration were obtained. It was found that for the same cooling load and cryogenic temperature, the performances of the two systems are almost the same, regardless of greater energy consumption of the combined vapour compression cycle.