A method of pumping a product by means of a dosing pump unit entails that two individually driven pump chambers, which are connected with a common outlet, are controlled in such a way that the suction phases of the pump chambers overlap each other so that the total inflow to the pump unit is maintained constant. A pump unit includes two pump chambers which have a common inlet and outlet. Communication between the pump chambers and the inlet and outlet is controlled by a valve body, having an inlet passage that is formed such that it can be oriented to connect both pump chambers with the inlet.