Pigmented aqueous basecoat material comprising a reaction product which is preparable by reaction of (a) at least one compound of the formula X 1 - Y - X 2 in which X 1, X 2, independently of one another, are each a functional group which is reactive toward epoxide groups, or hydrogen, with, however, at least one of the two groups X 1 and X 2 being a functional group which is reactive toward epoxide groups, and Y is a divalent aliphatic, aromatic or araliphatic hydrocarbon radical having a number-average molecular weight of 100 to 2500 g/mol, determined as specified in the description, with (b) at least one compound of the general structural formula in which R is a C 3 to C 6 alkylene radical and n is selected accordingly such that the compound (b) possesses an epoxide equivalent weight of 100 to 2000 g/mol, where components (a) and (b) are used in the reaction in a molar ratio of 2.3/0.7 to 1.7/1.6 and the resulting reaction product possesses a number-average molecular weight of 500 to 15 000 g/mol, determined as specified in the description, and an acid number of less than 10 mg KOH/g and also a hydroxyl number of 25 to 250 mg KOH/g, determined as specified in the description. (a) at least one compound of the formula X 1 - Y - X 2 in which X 1, X 2, independently of one another, are each a functional group which is reactive toward epoxide groups, or hydrogen, with, however, at least one of the two groups X 1 and X 2 being a functional group which is reactive toward epoxide groups, and Y is a divalent aliphatic, aromatic or araliphatic hydrocarbon radical having a number-average molecular weight of 100 to 2500 g/mol, determined as specified in the description, with X 1, X 2, independently of one another, are each a functional group which is reactive toward epoxide groups, or hydrogen, with, however, at least one of the two groups X 1 and X 2 being a functional group which is reactive toward epoxide groups, and Y is a divalent aliphatic, aromatic or araliphatic hydrocarbon radical having a number-average molecular weight of 100 to 2500 g/mol, determined as specified in the description, with (b) at least one compound of the general structural formula in which R is a C 3 to C 6 alkylene radical and n is selected accordingly such that the compound (b) possesses an epoxide equivalent weight of 100 to 2000 g/mol, where components (a) and (b) are used in the reaction in a molar ratio of 2.3/0.7 to 1.7/1.6 and the resulting reaction product possesses a number-average molecular weight of 500 to 15 000 g/mol, determined as specified in the description, and an acid number of less than 10 mg KOH/g and also a hydroxyl number of 25 to 250 mg KOH/g, determined as specified in the description. R is a C 3 to C 6 alkylene radical and n is selected accordingly such that the compound (b) possesses an epoxide equivalent weight of 100 to 2000 g/mol, where components (a) and (b) are used in the reaction in a molar ratio of 2.3/0.7 to 1.7/1.6 and the resulting reaction product possesses a number-average molecular weight of 500 to 15 000 g/mol, determined as specified in the description, and an acid number of less than 10 mg KOH/g and also a hydroxyl number of 25 to 250 mg KOH/g, determined as specified in the description.