A coated polymer foil is described and can be produced via coating of a polymer foil with an aqueous composition comprising (A) a polymer which is obtained via free-radical polymerization and which is composed of from 10 to 80% by weight of a compound selected from ethylenically unsaturated anhydrides and ethylenically unsaturated dicarboxylic acids, the carboxylic acid groups of which can form an anhydride group, and (B) an alkanolamine having at least two hydroxy groups. The coating gives the polymer foil an oxygen barrier and can in particular be used for producing packaging.