Abstract: The invention relates to a process for the production of two-coat finishes, in which a pigmented aqueous basecoat is applied, the basecoat obtained is coated over with a clearcoat, and basecoat and clearcoat are baked together. The process according to the invention is distinguished in that the aqueous basecoat contains an emulsion polymer which has been prepared in the presence of a reaction product (A), the reaction product (A) being obtained by reacting(i) a butadiene homo- or copolymer,(ii) at least one fatty acid of a drying oil or at least one drying oil or a mixture of at least one fatty acid of a drying oil and at least one drying oil, and(iii) maleic anhydridein a mass ratio of (i):(ii):(iii)=1.0:0.1 to 0.6:0.1 to 0.6 and, after adding a basic aqueous solution, converting the reaction product to an aqueous dispersion.