Abstract: In a method for operating a Stirling cycle process an operating medium is essentially compressed in an isothermal manner, subsequently heated in an isochoric manner subsequently expanded in an isothermal manner and subsequently cooled in an isochoric manner which completes the cycle process. In order to improve the energy efficiency of such processes for a clockwise power machine process and also for a counterclockwise refrigeration machine it is proposed that the isothermal compression be performed freely through a liquid piston compressor (2) and/or the isothermal expansion is performed by a liquid piston expander. Additionally a device for carrying out the method is disclosed.