Process for producing adhesive tapes, in which adhesive tapes coated on one side with an adhesive composition are subjected to radiation crosslinking, the irradiation of the adhesive tape taking place through the backing material of the adhesive tape into the adhesive composition in such a way that the backing material and that side of the adhesive composition facing the backing material receive a dose of from 30 to 200 kGy, and adjusting an acceleration voltage during the irradiation to create a dosage gradient through the adhesive tape such that the dose received on the open side of the adhesive composition has fallen to a range of from 0 to 20 kGy.