The present invention relates to a pigmented aqueous basecoat material comprising a reaction product which is preparable by reaction of (a) at least one aliphatic linear polyester having two functional end groups (a.1), with (b) at least one diene polymer having two functional end groups (b.1), where at least one type of group (a.1) is reacted in a linking manner with at least one type of group (b.1), said 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 1000 to 15 000 g/mol.