In a reciprocating-piston machine, in particular a refrigerant compressor for a motor vehicle air-conditioning system, including a machine shaft rotatably supported in a housing, a plurality of pistons arranged circularly around the machine shaft in the housing, and an annular pivoting disc driven by the machine shaft and engaging the pistons via a joint arrangement, the pivoting disc being connected in an articulated manner to the machine shaft via a driver for transmitting the machine shaft drive forces to the pistons and mounted on a machine shaft-supported sliding body so as to be pivotable about a hinge axis oriented transversely to the machine shaft, the sliding body has an elongated recess which is open at one axial end for receiving the driver and the sliding body further includes at its inside adjacent the machine shaft a cavity, which is in communication with a bore forming a discharge passage extending through the machine shaft.