An oscillating displacement pump, particularly a diaphragm pump (P) for liquid or gaseous delivery media, having a delivery space which on the one side is delimited by a pump head and on the other side by a delivery element, particularly formed by a diaphragm (6). The delivery element is drivingly connected to an eccentric drive, and an inlet valve connected to an inlet connection and an outlet valve connected to an outlet connection are connected to the delivery space. The pump has a pulsation damper (45) on the pressure side, and also an excess pressure limiting device (27) between the pressure and suction sides, these devices being integrated into the pump head. In use as a liquid pump, an oscillation chamber (16) is integrated into the suction side of the pump head. Pressure peaks are thereby diminished both on the suction side and the pressure side, and a pressure rise on the pressure side is limited to a predeterminable value.