A thermally vulcanizable pressure-sensitive adhesive comprising a chemically precrosslinked, pressure-sensitively adhesive polybutadiene-polyurethane and ground sulfur, which during the heating phase remains pressure-sensitively adhesive, does not liquefy and hence in this phase, in which the vulcanization has not yet started and the curing has not yet commenced, has shear strength at least under load to moderate low, is able to transmit forces and hence to perform holding, a process for producing it, an adhesive tape comprising this pressure-sensitive adhesive, and a process for producing the adhesive tape.