A medical balloon for attachment to a catheter tube, and method of making the balloon. The balloon comprises a plurality of co-extruded and coextensive layers of different polymeric materials (20A, 20B) at least one of which is a base structural layer (20B) and the other of which (20A) is formed of polyethylene and copolymers thereof or of SELAR. The base structural layer is thicker than the other layer.