Cohesive, rigid or elastic bandage which only adheres to itself and not to skin, hair and clothing, for fixing dressings, compression dressings and support dressings and permanently elastic compression and support dressings for medical purposes, wherein the bandage has bonded to both sides a cohesive substance, said bandage consisting of a web of weft and warp threads, and having fiber ends projecting from said web, said cohesive substance being fine particles of a size of 0.0000785 to 0.07 mm.sup.2 of an adhesive, bonded to said fiber ends on both sides of the web in a uniform distribution of 1,000 to 5,000 particles per approximately 500 mm.sup.2 in an application quantity in the order of magnitude of 10 to 40 g/m.sup.2, wherein there is substantially no reduction in the porosity and elasticity of the fabric.