A method for operating a reciprocating positive displacement pump for the simultaneous low-pulsation discharge of a plurality of liquids, having for each liquid at least two pump chambers and displacement devices capable of movement therein, of which the one displacement device takes in liquid during the actual discharge phase of the other displacement device, and at the end of its intake stroke reverses its direction of movement, and, in a pre-compression phase, pre-compresses the liquid taken into the associated pump chamber and when a predeterminable pre-compression pressure has been achieved comes to a standstill, and remains at the standstill until the other displacement device has ended its liquid discharge, and, subsequent to this discharge, begins its own discharge. The method includes the steps of carrying out a pressure compensation during the subsequent discharge stroke preventing a pressure compensation between the individual pump chambers during the subsequent discharge stroke.