Hemodialysis port assembly including a port and a catheter assembly. The port includes an inlet septum subtended by an inlet plenum and an outlet septum subtended by an outlet plenum. The catheter assembly includes an inlet channel connected to the inlet plenum and an outlet channel connected to the outlet plenum. The port and catheter assembly are completely implanted in the chest of a patient with the port subcutaneous and the end of the catheter assembly remote from the port injected into the subclavian vein. The blood flow in this vein is in the direction away from the end of the catheter assembly. Near this remote end the catheter assembly or the inlet channel terminates in an inlet valve and the outlet channel terminates in an outlet valve. Each of these valves is essentially a flapper on which the blood is incident in a generally perpendicular direction so that its flow is substantially unimpeded. The outlet valve is spaced a small but effective distance from the inlet valve in the downstream direction of the flow to toxified blood through the outlet channel. In practice of this invention, the detoxified blood from an artificial kidney is supplied to the vein through a hypodermic needle which penetrates the inlet septum, the inlet plenum, the inlet channel and the inlet valve and toxified blood is supplied from the vein to the artificial kidney through the outlet valve, the outlet channel, the outlet plenum and an outlet needle which penetrates the outlet septum. The spacing of the outlet valve from the inlet valve suppresses short-circuit flow of detoxified blood from the inlet branch to the outlet branch.