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Stirling engines have many unique advantages including higher thermal efficiencies, preferable exhaust gas characteristics, multi-fuel usage, and low noise and vibration. On the other hand, heat pump systems are very attractive for space heating and cooling and industrial usage. There are several environmental merits of Stirling-driven vapor-compression (SDVC) systems. A design method for the SDVC, which is based on mathematical methods for Stirling and Rankine cycles, has been developed. The model treats a kinematic Stirling engine and a scroll compressor which are coupled by a belt. The measured performance of an actual system well agreed with the calculated results. The attractive SDVC performance using conventional and alternative refrigerants was shown. From the calculated Total Equivalent Warming Impact, TEWI and operating costs, it became clear that the SDVC system with the alternative refrigerant has a higher potential as the future air-conditioning system.