Abstract: A process for haemodialysis, includes providing a dialyzer utilizing an electromagnetically controllable double membrane pump, whereby the membranes are each supported against an incompressible liquid during the stroke movement of a pump piston. The process includes filling the space between the membranes with the incompressible liquid, stroking the piston thereby sucking deaerated fresh dialysate through an opening in a front cover plate and into a first swept space bounded by one membrane and the front cover plate while simultaneously discharging used dialysate through an opening in a second cover plate and out of a second swept space bounded by the other membrane and the second cover plate. The pump piston then strokes to the other end of its range thereby discharging the fresh dialysate through another opening of the front end cover plate, and sucking used dialysate through another opening of the second cover plate.