A decsription is given of an aqueous copolymer poly(vinyl ester) dispersion comprising A) 100 parts by weight of a copolymer derived from A1) from 34.9 to 95% by weight of vinyl esters of aliphatic, saturated carboxylic acids, A2) from 4.9 to 65% by weight of maleic esters and/or fumaric esters of monohydric aliphatic alcohols having a chain length of C.sub.1-C.sub.18 and/or alpha-olefins having from 2 to 8 carbon atoms, A3) from 0.1 to 10% of at least one comonomer having at least one stabilizing nonionic or ionic group, and also A4) if appropriate, other comonomers, the sum of components A1, A2 and A3 and if appropriate A4 giving 100% by weight, B) from 0.1 to 4.5 parts by weight, based on the total amount of the monomers used, preferably from 0.5 to 3.5 parts by weight of at least one protecting colloid, preferably poly(vinyl alcohol), C) from 0.1 to 10 parts by weight, based on the total amount of the monomers used, preferably from 0.5 to 5.0 parts by weight, of a nonionic emulsifier, and D) if appropriate, further additives suitable for coating foods. The dispersion is produced by free-radical emulsion polymerization and is suitable for coating foods. The films formed from these dispersions are distinguished by a low water-vapor transmission rate.