Radiation-curable, polyester acrylate-containing compositions (I) obtainable by reacting 0.5 to 20 mol % of a polyester polyol (A) and 0.5 to 30 mol % of a polyester diol (B) with 1 to 10 mol % of phthalic anhydride (C) and 65 to 75 mol % of (meth)acrylic acid (D) in the presence of an acidic esterification catalyst, a hydrocarbon (L), and a polymerization inhibitor. Reaction temperatures range from 60 to 140° C. The hydrocarbon (L) functions as solvent, forms an azeotropic mixture with water, and is removed distillatively after esterification. Water formed in the reaction is removed azeotropically. After neutralization of the esterification catalyst, free (meth)acrylic acid is reacted with an epoxide compound (E) in an amount equivalent to the acid number of the reaction mixture. The compound (E) has at least two epoxide groups per molecule. The compositions are suitable for coating the surfaces of solid substrates.