The present invention relates to a method for producing a multicoat paint system on a metallic substrate, in which a basecoat or a plurality of directly successive basecoats are produced directly on a metallic substrate coated with a cured electrocoat, a clearcoat is produced directly on the one basecoat or the uppermost of the plurality of basecoats, and then the one or more basecoats and the clearcoat are jointly cured, and wherein at least one basecoat material used for production of the basecoats comprises at least one aqueous dispersion comprising at least one copolymer (CP), said copolymer (CP) being preparable by initially charging an aqueous dispersion of at least one polyurethane, and then polymerizing a mixture of olefinically unsaturated monomers in the presence of the polyurethane from (i), in which a water-soluble initiator is used, the olefinically unsaturated monomers are metered in such that a concentration of 6.0% by weight, based on the total amount of olefinically unsaturated monomers used for polymerization, in the reaction solution is not exceeded over the entire reaction time, and the mixture of the olefinically unsaturated monomers comprises at least one polyolefinically unsaturated monomer, and comprises at least one linear hydroxy-functional reaction product (R) having an acid number less than 20 mg KOH/g, the preparation of which involves using at least one compound (v) containing two functional groups (v.1) and an aliphatic or araliphatic hydrocarbyl radical (v.2) which is arranged between the functional groups and has 12 to 70 carbon atoms.