The invention relates to an apparatus for extracorporeal blood treatment that comprises a device 1 for providing fresh dialysate and a drain 2 for used dialysate, a balancing device 4 for balancing fresh dialysate and used dialysate, an ultrafiltration device 15, and a dialyser 3 that is divided into a blood chamber 6 and a dialysate chamber 7 by a semi-permeable membrane 5. The invention further relates to a method for operating such an apparatus for extracorporeal blood treatment. The apparatus according to the invention is based on the use of the ultrafiltration device 15 of the blood treatment apparatus for raising the liquid level in the air separation device 12 on the secondary side of the dialysate system I. In the apparatus according to the invention, the ultrafiltration device 15 is designed such that the ultrafiltration device can be operated not only in an ultrafiltration mode, but also in a ventilation mode. In the ultrafiltration mode, the ultrafiltration device 15 is operated in such a way that used dialysate is removed from the container 12A of the first air separation device 12 whereas in a ventilation mode the ultrafiltration device 15 is operated in the opposite direction so that used dialysate is supplied into the container 12A of the first air separation device 12, as a result of which the liquid level 12D rises in the container of the first air separation device.