The pump is provided with a plurality of pumping chambers and electrically activatable valves. An elastic membrane is arranged in each pumping chamber and divides the same into a first and a second chamber section. Each valve is connected to the second chamber section of a pumping chamber. When a pressure drop is applied over the valve and the valve is activated (i.e. opened), the pressure in the second chamber section changes, which causes the membrane to move, which in turn leads to a change of the volumes of both chamber sections. This e.g. allows to pump well-defined amounts of fluid from the chamber sections to a drug dispensing device.