A catheter tubing (2) consists of a composite comprising a first material (54) which mainly consists of a hydrophilic plastic material which absorbs moisture and which therefore swells in contact with e.g. blood, and a second material which essentially does not absorb moist but which forms reinforcing longitudinal strands (55) in the catheter tubing, which counteract that the catheter tubing is extended or becomes thicker because of the swelling capacity of the first polymeric material, such that the volume increase of the hydrophilic, first plastic material substantially results in an increase of the circumference of the tubing and hence of its diameter and flow area. A catheter is made of a catheter tubing of that type and can be included in an assembly (1) comprising a hub (4) having a front portion (11) provided with a pair of wings (29) extending outwards from the hub. The wings can be folded against one another in order to serve as a gripping member (7) provided adjacent to the catheter when the catheter is being inserted into a fistula (40), whereupon they can be brought to contact and be releasably adhered to the skin of a patient.
