A method of making a dual lumen catheter which is a unitary, elongated, flexible catheter tube that is substantially circular in cross-section. The catheter tube has an outer wall member forming a tube having a proximal end and a distal end portion adapted for insertion within a vein or artery of a patient. The outer wall member defines first and second coaxial lumens that are separated by an inner common support wall which is substantially circular and joins the outer wall. The first lumen extends longitudinally between the opposed distal and proximal ends of the catheter tube and terminates coextensive with the distal end portion of the catheter tube. The second lumen extends longitudinally from the proximal end of the catheter tube and terminates proximal to the distal end portion of the catheter tube. The second lumen is crescent-shaped in cross-section and substantially surrounds the first lumen. The cross-sectional areas of the first and second lumens are approximately equal. Each of the first and second lumens are totally smooth internally, thereby containing no ridges or connections which can promote formation of blood clots or cause hemolysis or damage to red blood cells during dialysis. The catheter tube is secured at its proximal end to the distal end of a hollow hub assembly.