A capillary dialyzer comprising: a) a housing defining a longitudinally extending internal chamber including a first end and a second end; b) a bundle of semi-permeable hollow fiber membranes disposed within the internal chamber and extending longitudinally from the first end of the housing to the second end of the housing, the hollow fiber membranes having an outer surface, and a first end and a second end corresponding to the first end and the second end of the internal chamber; c) end wall means supporting the first and second ends of the hollow fiber membranes within the internal chamber so as to sealingly separate the first and second ends of the hollow fiber membranes from the outer surface of the hollow fiber membranes between the first and second ends thereof; d) a first end cap covering the first end of the housing and a second end cap covering the second end of the housing, the first and second end caps being applied to the first and second ends of the housing in a fluid-tight manner; and the first and second end caps ( 4a, 4b) having a circular groove which receives the wall of the housing and comprises indentations, which create a fluid connection between the inside of the capillary dialyzer and its exterior when the end caps ( 4a, 4b) are mounted on the housing but have not yet been welded to the housing; e) an inlet for the introduction of a fluid into the internal chamber and an outlet for the evacuation of a fluid from the internal chamber at a location between the first and second end of the housing; f) support rings disposed between the end wall means and the housing at the first and second ends of the internal chamber; and g) sealing rings interposed between the end wall and the first end cap and between the end wall and the second end cap, respectively; characterized in that the header sections of the housing comprise notches on the inside surface which extend from the mouth of the housing to the end of a ledge inside the housing on which the support ring is positioned. a) a housing defining a longitudinally extending internal chamber including a first end and a second end; b) a bundle of semi-permeable hollow fiber membranes disposed within the internal chamber and extending longitudinally from the first end of the housing to the second end of the housing, the hollow fiber membranes having an outer surface, and a first end and a second end corresponding to the first end and the second end of the internal chamber; c) end wall means supporting the first and second ends of the hollow fiber membranes within the internal chamber so as to sealingly separate the first and second ends of the hollow fiber membranes from the outer surface of the hollow fiber membranes between the first and second ends thereof; d) a first end cap covering the first end of the housing and a second end cap covering the second end of the housing, the first and second end caps being applied to the first and second ends of the housing in a fluid-tight manner; and the first and second end caps ( 4a, 4b) having a circular groove which receives the wall of the housing and comprises indentations, which create a fluid connection between the inside of the capillary dialyzer and its exterior when the end caps ( 4a, 4b) are mounted on the housing but have not yet been welded to the housing; e) an inlet for the introduction of a fluid into the internal chamber and an outlet for the evacuation of a fluid from the internal chamber at a location between the first and second end of the housing; f) support rings disposed between the end wall means and the housing at the first and second ends of the internal chamber; and g) sealing rings interposed between the end wall and the first end cap and between the end wall and the second end cap, respectively;