A method for the production of adhesive tape with crosslinked polyacrylate hot-melt adhesive by adding a crosslinker to a polyacrylate melt, coating onto a base strip and crosslinking, involves using a thermal crosslinker and a copolymer in which some of the (meth)acrylate ester monomer units contain prim. hydroxyl groups. A method for the production of adhesive tape with a crosslinked acrylate hot-melt adhesive on one or both sides, in which a crosslinker is added, in the melt, to a polyacrylate copolymer based on (meth)acrylate esters, the mixture is coated onto a strip-like base and then homogeneously crosslinked. In this method, the crosslinker is a thermal crosslinker and some of the (meth)acrylate ester units contain prim. hydroxyl groups. An independent claim is also included for adhesive tape with a homogeneously-crosslinked layer of polyacrylate, preferably obtained by this method.