a method is provided for controlling an intermittently supercritically operating refrigeration circuit . a control valve is controlled : in the subcritical mode , so that a predetermined “ subcritical pressure ” ensuring a predetermined sub - cooling of the liquid refrigerant at the outlet of a heat - rejecting heat exchanger is maintained ; in the supercritical mode , so that a predetermined “ supercritical pressure ”, which is optimized for optimum efficiency , of the supercritical refrigerant at the outlet of the heat - rejecting heat exchanger is maintained ; and in a border mode in a border region next to the critical point , dependent on a “ continuity pressure ” which is determined on the basis of the predetermined “ subcritical pressure ” and the predetermined “ supercritical pressure ” of steps and .