The invention relates to a process for the production of two-coat finishes, in which a pigmented basecoat is first applied, the resulting basecoat film is coated with a powder clearcoat, and basecoat and clearcoat are subsequently baked together. In accordance with the invention, the powder clearcoat employed is a powder coating which contains an epoxide group-containing polyacrylate resin as binder and a mixture of (A) a polyanhydride and (B) a carboxyl group-containing polyester resin as crosslinking agent. The polyester resin can be prepared by reacting a diol (b1), a compound (b2) which contains per molecule at least three functional groups selected from hydroxyl, primary amino, secondary amino, carboxyl and acid anhydride groups, and (b3) a dicarboxylic acid in a molar ratio of (b1): (b2): (b3)=0.0 to 3.0: 1.0: 1.5 to 9.0 to give a polyester resin having an acid value of 40 to 300.