Compressor device, comprising: a first compressor stage, including: a first compressor chamber having a defined volume in which a first metal bellows sub-divides the first compressor chamber into a first gas volume with a working gas and a first liquid volume with a working liquid, a first high-pressure and a first low-pressure working gas connection (18-1, 20-1) that lead to the first gas volume, and a first working liquid connection leading to the first liquid volume; and a pump device periodically pumping the working liquid via the first working liquid connection into the liquid volume, thereby compressing the working gas in the gas volume periodically, characterized in that a second compressor stage is provided including a second compressor chamber that is sub-divided by a second metal bellows into a second gas volume with working gas and a second liquid volume with working liquid, that the second compressor stage includes a second high-pressure working gas connection and a second low-pressure working gas connection (18-2, 20-2) leading into the second gas volume, that the second compressor stage includes a second working liquid connection leading into the second liquid volume, that the pump device is a common pump device, that the common pump device is connected with the second compressor stage via the second working liquid connection, that the second low-pressure working gas connection of the second compressor stage is connected with a buffer storage via a first gas line and a first lock valve, and that the first high-pressure working gas connection of the first compressor stage is connected with the buffer storage via a second gas line. a first compressor stage, including: a first compressor chamber having a defined volume in which a first metal bellows sub-divides the first compressor chamber into a first gas volume with a working gas and a first liquid volume with a working liquid, a first high-pressure and a first low-pressure working gas connection (18-1, 20-1) that lead to the first gas volume, and a first working liquid connection leading to the first liquid volume; and a first compressor chamber having a defined volume in which a first metal bellows sub-divides the first compressor chamber into a first gas volume with a working gas and a first liquid volume with a working liquid, a first high-pressure and a first low-pressure working gas connection (18-1, 20-1) that lead to the first gas volume, and a first working liquid connection leading to the first liquid volume; and a pump device periodically pumping the working liquid via the first working liquid connection into the liquid volume, thereby compressing the working gas in the gas volume periodically, characterized in that a second compressor stage is provided including a second compressor chamber that is sub-divided by a second metal bellows into a second gas volume with working gas and a second liquid volume with working liquid, that the second compressor stage includes a second high-pressure working gas connection and a second low-pressure working gas connection (18-2, 20-2) leading into the second gas volume, that the second compressor stage includes a second working liquid connection leading into the second liquid volume, that the pump device is a common pump device, that the common pump device is connected with the second compressor stage via the second working liquid connection, that the second low-pressure working gas connection of the second compressor stage is connected with a buffer storage via a first gas line and a first lock valve, and that the first high-pressure working gas connection of the first compressor stage is connected with the buffer storage via a second gas line.