A multi-stage compressor (1) for compressing gases with a low-pressure region (2) and a high-pressure region (5), wherein at least one rotary compressor (3) is provided in the low-pressure region (2), and at least one reciprocating piston compressor (6) with two cylinders (7) is provided in the high-pressure region (5), and wherein a common engine (4) is provided for driving the rotary compressor (3) and the reciprocating piston compressor (6), wherein the cylinders (7) are arranged to be rotated relative to each other by 180° in the high-pressure region (5).