Process for preparing crosslinked pressure-sensitive adhesives at least partly based on block copolymers comprising at least one polyvalent thioether unit, characterized in that at least the following process steps are carried out:two-stage or multi-stage free-radical addition polymerization of at least two copolymerizable monomers in the presence of at least one polyvalent mercaptan, at least one of the monomers being functionalized such that on irradiation with ultraviolet rays it initiates a UV crosslinking,the polymerization producing block copolymers containing at least one polyvalent thioether unit,coating of the polymer from the melt onto a backing,crosslinking of the polymer on the backing by irradiation with ultraviolet radiation.