Abstract: The invention relates to copolymers containing carboxyl groups and having an acid number of 20 to 150 mg of KOH/g and a number average molecular weight of 2000 to 8000, which can preferably be prepared from copolymers containing hydroxyl groups by reaction with carboxylic anhydrides, to a process for their preparation and their use in coating agents. The copolymers contain a vinyl ester, a vinyl aromatic, a hydroxyalkyl ester of an .alpha.,.beta.-unsaturated carboxylic acid, and optionally other monomers that may contain acid groups.