Abstract: The pump unit according to the invention encompasses at least two piston pumps, which include pump cylinders and pump pistons. Each piston pump comprises at least one inlet valve and an outlet valve. At least the inlet valves, but optionally also the outlet valves, are embodied as springless ball check valves, in the case of which the valve ball is located in an interior, which is defined by a surface of the housing (preferably of the first housing part 11) at least on one side. With this design, the actual check valve is only joined and is thus produced completely only when the housing parts are brought together. Check valves, which can be sterilized well and which can be cleaned without any residue, can thus be integrated into the pump unit in a simple and reliable manner.