The invention embraces basecoating compositions comprising as binder constituents (i) an acrylate dispersion having a content of from 30 to 60% by weight of C1-C8-alkyl (meth)acrylate-containing monomers, from 30 to 60% by weight of vinylaromatic monomers and from 0.5 to 10% by weight of (meth)acrylic acid in the polymer, and (ii) a dispersion of a polymer which is obtainable by subjecting an ethylenically unsaturated monomer or a mixture of ethylenically unsaturated monomers to free-radical polymerization in the presence of a water-insoluble initiator or of a mixture of water-insoluble initiators and in an aqueous dispersion of a polyurethane resin which has a number-average molecular weight Mn of from 1000 to 30,000 daltons and comprises on average from 0.05 to 1.1 polymerizable double bonds per molecule, the weight ratio between the polyurethane resin and the ethylenically unsaturated monomers or the mixture of ethylenically unsaturated monomers lying between 1:10 and 10:1, and (iii) a Theological assistant which comprises a synthetic polymer having ionic and/or associative groups. Also embraced are processes for producing multicoat coating systems with coats of the said basecoating compositions, and substrates coated with such multicoat coating systems.