The present invention relates to a refrigerating system and a method of operating a refrigerating system. The refrigerating system includes a compressor, a gas cooler used as a heat-dissipation type heat exchanger, an expansion valve used as a throttling means, an evaporator used as a heat-absorption type heat exchanger and an accumulator, which are connected in series with each other to form a closed circuit. The closed circuit is adapted so that the higher pressure of the closed circuit becomes the supercritical pressure of a refrigerant circulating the closed circuit. This has a control characteristic property wherein the lower evaporating pressure increases as the higher pressure increases. The lower evaporating pressure and the higher pressure are detected, respectively, and if the detected value of the lower evaporating pressure is lower than a target value for the lower evaporating pressure determined based on the above control characteristic property in correspondence to the detected value of the higher pressure, the discharge capacity of the compressor is reduced so that the lower evaporating pressure coincides with the target value.