The invention relates to a method of coating articles with powder coatings which contain polymers and are applied to the surface of the substrate to be coated, are melted and are crosslinked by UV radiation, the polymers employed being copolymers of(a) at least one monomer of the general formula (I)CH.sub.2 .dbd.C(R.sup.1)--CO--OR.sup.2 (I) whereR.sup.1 =H or CH.sub.3 andR.sup.2 =H, C.sub.n H.sub.2n+1 where n=from 1 to 30, or is an alicyclic, araliphatic or heterocyclic radical, hydroxyalkyl, alkoxyalkyl, glycidyl or aminoalkyl, or of the general formula IICH.sub.2 .dbd.C(R.sup.1)--CO--NR.sup.3 R.sup.4 (II) where R.sup.3 =H or CH.sub.3 and where R.sup.3 and R.sup.4 may be identical to or different from one another and are H, CH.sub.2 OH, C.sub.n H.sub.2n+1 where n=1 to 30(b) at least one copolymerizable, ethylenically unsaturated, organic compound which is different from (a)and(c) at least one copolymerizable, ethylenically unsaturated, aromatic or partially aromatic ketone which is capable of abstracting hydrogen in the excited triplet state.