A reciprocating-piston compressor having at least two working cylinders arranged in series, along a cylinder axis is described. The compressor includes a piston in each of the cylinders, guided in an axially movable manner, and a common axially actuated piston rod of the pistons, extending through a passage opening in a partition between the at least two working cylinders. The at least two working cylinders are sealed off with respect to one another in a region of the common axially actuated piston rod, exclusively by a non-contact seal. The axial seal has an axial gap seal formed between a radially outer circumferential surface of the common axially actuated piston rod and a radially inner circumferential surface of the passage opening.