A device for extracorporeal blood treatment and a method for operating an extracorporeal blood treatment device provide for an ultrafiltrate pump of an ultrafiltration apparatus to be operated in a first and second operating mode. The ultrafiltrate pump is operated in the first operating mode in such a way that the pressure on the blood-side of the semipermeable membrane is higher than the pressure on the dialysate-side of the semipermeable membrane of a dialyser, so that during the first operating mode a predetermined amount of fluid is removed from an extracorporeal blood circuit via the semipermeable membrane of the dialyser. In the second operating mode, the ultrafiltrate pump is operated in such a way that the pressure on the blood-side of the semipermeable membrane is, at successive intervals, alternately higher and lower than the pressure on the dialysate-side of the semipermeable membrane of the dialyser, so that fluid is continuously removed from and supplied to the extracorporeal blood circuit via the semipermeable membrane (push/pull mode). Additional components, in particular a separate push/pull pump, are not required for operation of the blood treatment device in push/pull mode. This results in both lower dimensions and lower weight. Operation in push/pull mode can increase the service life of the dialyser and the clearance of the dialysis treatment can also be increased for certain substances.