The pump unit (10) according to the invention has a particularly simple design, which includes just two housing parts (14, 15) and also four valve closure members (37) and pump pistons (25, 29). The valve closure members (37) are preferably identical to one another and are trapped in a pocket between both housing parts (14, 15). The housing parts (14, 15) are preferably permanently interconnected by means of an ultrasonic weld seam. The valve closure members are formed by disc-like or plate-like plastic parts, which are resilient per se and which may optionally have a central pin (42) as an assembly and orientation aid. As desired, the valve closure members bear against their respective valve seat (43) with or without bias and form valves which open and close particularly reliably, are responsive to the slowest flow velocities and can be easily sterilised.
