A multilayer element comprising a substrate, an intermediate layer and a photopolymerizable or photocrosslinkable layer in the stated order is used for producing printing or relief plates. The intermediate layer contains a copolymer of a monomer (A) of the formula (I) or (II) and a copolymerizable monomer (B) ##STR1## where R.sup.1 is vinyl, propen-2-yl, 1-buten-2-yl or styryl or a radical R.sup.2 --O--CO--CH.dbd.CH--, R.sup.2 is an alkyl, aryl, aralkyl or cycloalkyl radical of up to 10 carbon atoms, R.sup.3 is H, methyl or ethyl and n is from zero to 5. The intermediate layer in the multilayer element has improved adhesion in the laminate. It is initially nontacky and does not become tacky until after the application of the photopolymerizable layer, as a result of the interaction with said layer. The improved adhesion in the laminate is retained even after storage and repeated use of the finished printing plates.