Abstract: Method and apparatus for extracorporeally dialyzing the blood of a patient with only a single venipuncture including withdrawing blood from the patient through the venipuncture and forcing the blood along an arterial path to a dialyzer. Blood emerging from the dialyzer is then conducted along a venous path again to the venipuncture. The pressure is monitored in the extracorporeal system to trigger occluding devices which alternately open and close the arterial and venous paths so that undialyzed blood is taken from the patient and dialyzed blood is injected into the patient. The apparatus includes clamps actuated by a pressure monitor to alternately obstruct the arterial and venous paths. A blood pump may be controlled to operate as one of the clamps. In an alternative embodiment, blood is circulated at a comparatively high flow rate throughout the system. A clamp is provided in one of the arterial or venous lines, said clamp being controlled by a pressure monitor.