A throughput-adjustable fluid-displacement machine includes a stator and a rotor which is supported on the stator for rotation about an axis. The stator has two axially spaced circumferentially extending cam tracks and the rotor has two sets of passages therein, each of the passages having an open end which always faces a different one of the cam tracks for each of the sets of passages. A plurality of pistons is respectively accommodated in the above-mentioned passages, each of the pistons having a cam follower portion and being acted on by a spring which urges the cam follower portion into a constant contact with the respective cam track so that the piston reciprocates in dependence on the configuration of the respective cam track. Two control sleeves, one for each of the sets of passages, is interposed between and selectively communicates the working chambers of the respective passages with respective input and output conduits of the machine. An angularly displacing arrangement is provided which displaces the two control sleeves simultaneously but in opposite directions whereby the throughput of the machine is adjusted while maintaining a substantially pulsation-free flow through the conduits. Preferably, the two control sleeves are displaced at the same angles in the opposite directions.