Powder coating compositions based on A) copolymers prepared from olefinically unsaturated monomers, containing epoxide and anhydride groups and having a glass transition temperature T.sub.g of 30.degree. to 80.degree. C., an average molecular weight M.sub.n of 1,000 to 6,000 and a molecular weight distribution M.sub.w /M.sub.n of 2.5 to 10.0, B) a hardener component selected from (i) (cyclo)aliphatic dicarboxylic acids, (ii) anhydrides of such dicarboxylic acids, (iii) polyol-modified polymeric anhydrides of such dicarboxylic acids and (iv) aliphatic hydroxycarboxylic acids and optionally C) additional crosslinking agents in the form of polyaddition products having uretidione groups, and the use of these compositions for coating heat-resistant substrates.