A compressor device that periodically supplies compressed working gas to a cooling device loses less of the gas by not using rotary valves. The compressor device includes a compressor cylinder, a compensation container and a drive device with an hydraulic cylinder. The compressor cylinder includes a compressor element, such as a piston or membrane, that divides the compressor cylinder into first and second volumes. The first volume contains the gas that is compressed by the compressor element. The hydraulic cylinder has a piston that is coupled to the compressor element. The compensation container contains compensation fluid and is directly connected to the second volume. The compensation container is also connected to the first volume by a gas line with a non-return valve that opens in the direction of the first volume. The drive device allows the compressed gas to be provided at a frequency required for Gifford-McMahon and pulse-tube coolers.