Abstract: A blood dialyzing apparatus having a dialyzer with blood and dialysate chambers defined therein comprises a blood pump for pumping the blood from a cannula, pierced in the patient's A-V fistula, back to the patient's A-V fistula through the blood chamber of the dialyzer, and a fluid circuit for the supply of a dialyzing solution past the dialysate chamber. The fluid circuit includes first and second shut-off valves disposed adjacent the inlet and outlet of the dialysate chamber, respectively, while a pressure sensor is provided to detect the pressure of the blood flowing upstream of the blood pump and also upstream of the blood chamber. When the pressure of the blood so detected attains a value equal to or lower than a predetermined value, the first and second shut-off valves are closed on the one hand and the ultrafiltration pressure in the dialyzer becomes substantially zero.