Method for producing a multicoat paint system on a metallic substrate, comprising producing a cured electrocoat (E.1) on the metallic substrate by electrophoretic application of an electrocoat (e.1) to the substrate and subsequent curing of the electrocoat (e.1), producing (2.1) a basecoat (B.2.1) or (2.2) a plurality of directly successive basecoats (B.2.2.x) directly on the cured electrocoat (E.1) by (2.1) applying an aqueous basecoat material (b.2.1) directly to the electrocoat (E.1) or (2.2) applying a plurality of basecoat materials (b.2.2.x) in direct succession to the electrocoat (E.1), producing a clearcoat directly on (3.1) the basecoat (B.2.1) or (3.2) an uppermost basecoat (B.2.2.x) by applying a clearcoat material (k) directly to (3.1) the basecoat (B.2.1) or (3.2) the uppermost basecoat (B.2.2.x), jointly curing (4.1) the basecoat (B.2.1) and the clearcoat or (4.2) the basecoats (B.2.2.x) and the clearcoat, characterized in that the basecoat material (b.2.1) or at least one of the basecoat materials (b.2.2.x) comprises the following components: at least one aqueous dispersion comprising at least one copolymer, said copolymer being preparable by (i) initially charging an aqueous dispersion of at least one polyurethane, and then (ii) polymerizing a mixture of olefinically unsaturated monomers in the presence of the polyurethane from (i), in which (a) a water-soluble initiator is used, (b) 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 (c) the mixture of the olefinically unsaturated monomers comprises at least one polyolefinically unsaturated monomer, at least one linear hydroxy-functional reaction product 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.a) and an aliphatic or araliphatic hydrocarbyl radical (v.b) which is arranged between the functional groups and has 12 to 70 carbon atoms, and at least one polyurethane resin, the preparation of which involves using at least one compound (x.1) containing at least one carboxylic acid group and at least one group reactive toward isocyanate groups. producing a cured electrocoat (E.1) on the metallic substrate by electrophoretic application of an electrocoat (e.1) to the substrate and subsequent curing of the electrocoat (e.1), producing (2.1) a basecoat (B.2.1) or (2.2) a plurality of directly successive basecoats (B.2.2.x) directly on the cured electrocoat (E.1) by (2.1) applying an aqueous basecoat material (b.2.1) directly to the electrocoat (E.1) or (2.2) applying a plurality of basecoat materials (b.2.2.x) in direct succession to the electrocoat (E.1), producing a clearcoat directly on (3.1) the basecoat (B.2.1) or (3.2) an uppermost basecoat (B.2.2.x) by applying a clearcoat material (k) directly to (3.1) the basecoat (B.2.1) or (3.2) the uppermost basecoat (B.2.2.x), jointly curing (4.1) the basecoat (B.2.1) and the clearcoat or (4.2) the basecoats (B.2.2.x) and the clearcoat, at least one aqueous dispersion comprising at least one copolymer, said copolymer being preparable by (i) initially charging an aqueous dispersion of at least one polyurethane, and then (ii) polymerizing a mixture of olefinically unsaturated monomers in the presence of the polyurethane from (i), in which (a) a water-soluble initiator is used, (b) 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 (c) the mixture of the olefinically unsaturated monomers comprises at least one polyolefinically unsaturated monomer, (i) initially charging an aqueous dispersion of at least one polyurethane, and then (ii) polymerizing a mixture of olefinically unsaturated monomers in the presence of the polyurethane from (i), in which (a) a water-soluble initiator is used, (b) 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 (c) the mixture of the olefinically unsaturated monomers comprises at least one polyolefinically unsaturated monomer, (a) a water-soluble initiator is used, (b) 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 (c) the mixture of the olefinically unsaturated monomers comprises at least one polyolefinically unsaturated monomer, at least one linear hydroxy-functional reaction product 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.a) and an aliphatic or araliphatic hydrocarbyl radical (v.b) which is arranged between the functional groups and has 12 to 70 carbon atoms, and at least one polyurethane resin, the preparation of which involves using at least one compound (x.1) containing at least one carboxylic acid group and at least one group reactive toward isocyanate groups.