Abstract: A process is disclosed for preparing bioactive, covalently fixed coatings on the surfaces of substrates, by grafting to a surface of the substrate a coating polymer which contains the following monomers in copolymerized form: (i) at least one monomer of the general formula: R—(A)a  (I), in which R is a mono- or diolefinically unsaturated organic radical having a valence a, A is a carboxyl group, a sulfuric acid group, a sulfonic acid group, a phosphoric acid group, a phosphonic acid group, a phosphorous acid group, a phenolic hydroxyl group, or a salt of one of these acid groups, and a is 1, 2 or 3; and (ii) at least one monomer which is sensitive to UV radiation.