The invention relates to a process for the preparation of a two-coat finish on a substrate surface, in which process a basecoat is employed which contains as binder a polymer which can be obtained by subjecting an ethylenically unsaturated monomer or a mixture of ethylenically unsaturated monomers to free-radical polymerization in an aqueous dispersion of a polyurethane resin which has a number-average molecular weight of from 1000 to 30,000 and contains on average from 0.05 to 1.1 polymerizable double bonds per molecule, and in the presence of a water-insoluble initiator or of a mixture of water-insoluble initiators, the weight ratio of the polyurethane resin to the ethylenically unsaturated monomer or to the mixture of ethylenically unsaturated monomers being between 1:10 and 10:1.