A process for the preparation of copolymers in which in a first step an olefinically unsaturated dicarboxylic acid is reacted with a polyhydric alcohol to yield a hemi-ester having free hydroxyl groups, which in a second step is reacted with a monoepoxy compound to yield an olefinically unsaturated diester containing hydroxyl groups, wherein the diester is copolymerized in at least one further step with at least one unsaturated monomer having no free carboxyl groups, and the hardenable reaction product thus obtained is either isolated or hardened with a hardening agent, and coating and adhesive compositions containing a copolymer thus obtained.