Abstract: A low-pulsation displacement pump comprises two series-connected cylinders which are controlled by valves so that the delivery takes place only in one direction. The pistons of the cylinders are controlled through cams which are driven jointly at a constant velocity. The cams are so formed that the transition phase preceding the delivery phase (in the direction of delivery) of the after-cylinder is longer than the transition phase preceding the delivery phase (delivery direction) of the forward cylinder. In another embodiment, the transition phase preceding the delivery phase of the after-cylinder is greater than 60.degree.. A further embodiment comprises combining the transition phase preceding the delivery phase of the after-cylinder with an isocratic phase and an overlapping phase.