Dialysis device comprising: an arterial blood duct (18) for supplying blood from a patient to a dialyzer (16)； a venous blood duct (20) to return dialyzed blood from the dialyzer to the patient； a controller that controls a dialysate distribution pump (12, 14) for pumping new dialysate into the dialyzer and dialysate used outside the dialyzer, the dialysate distribution pump having an inlet conduit for receiving new dialysate from a dialysate supply ( 30)； a pressure sensor (37, 39) in the arterial and / or venous blood conduit, the sensor being operatively connected to the controller so that the controller receives a signal from the sensor representative of the pressure in the arterial and / or venous blood； wherein, the controller monitors the sensor signal in the arterial and / or venous blood conduit and controls the dialysate pressure in the inlet conduit of the dialysate distribution pump in response to the pressure measured in the blood conduit arterial and / or venous, in which the device includes a dialysate supply pump (60) having an outlet fluidly connected to the dialysate distribution pump inlet duct, the dialysate supply pump being able to pump dialysate inside the inlet conduit of the dialysate distribution pump at a predetermined pumping pressure set by the controller in response to the pressure measured in the arterial and / or venous blood conduit, in which the dialysate supply pump is a membrane pump having a pump cavity covered by a flexible membrane, in which the pump can be operated by actuating the membrane, in e l that the diaphragm pump can be operated pneumatically.Dispositivo de diálisis que comprende: un conducto de sangre arterial (18) para suministrar sangre de un paciente a un dializador (16)； un conducto de sangre venosa (20) para devolver sangre dializada del dializador al paciente； un controlador que controla una bomba de distribución de dializado (12, 14) para bombear dializado nuevo dentro del dializador y dializado usado fuera de
