Pulse tube coolers and Gifford-McMahon coolers are used to cool nuclear spin tomographs and cryopumps. To supply cooled working gas, gas compressors and in particular helium compressors are used with rotational or rotary valves. The rate at which compressed helium is introduced into the cooling device and let out again lies in the range of 1 Hz. A problem of conventional screw or piston processors is that oil from the compressor mixes with the working gas and thus contaminates the cooling device. By providing a second compressor stage, a common pump device can be used to pump in both directions, which results in a two-stage compressor device. The working gas is compressed in each flow direction of the working liquid, in one flow direction in the first compressor stage and in the opposite flow direction in the second compressor stage. Thus, the efficiency of the compressor device is improved.