An extracorporeal blood treatment apparatus having a fluid system and a pump for conveying fluid in the fluid system, wherein the pump is a non-occluding pump, and a method for shutting off or reducing the speed of rotation of a non-occluding pump in a fluid system of an extracorporeal blood treatment apparatus. The apparatus and the method are characterized in that before the speed of rotation is reduced or the pump is shut off, the fluid flow into the feed line and out of the discharge line is first interrupted, and after a predetermined time interval after interruption of the fluid flow has elapsed, the speed of rotation of the pump is reduced or the pump is shut off. The time-delayed shut-off of the pump prevents a reverse flow of fluid, particularly of blood into the arterial blood line, even in the absence of occlusion. As a result of the time-delayed shut-off or reduction in the speed of rotation of the pump, however, an excess pressure is produced in the fluid system. Therefore the blood treatment apparatus and the method provide for counter-measures to prevent uncontrolled fluid flow when the shut-off elements are opened, due to the excess pressure.
