Packaging materials are produced by a process which comprises coating substrates suitable for packaging with an aqueous solution or emulsion which contains a copolymer A) composed ofa) from 10 to 100% by weight of an ethylenically unsaturated C.sub.3 -C.sub.5 -carboxylic acid or C.sub.3 -C.sub.5 -di-carboxylic acid or anhydrides or half-esters of the dicarboxylic acids,b) from 0 to 50% by weight of an ethylenically unsaturated compound having at least one sulfo or sulfonate group andc) from 0 to 70% by weight of further monomers,and a polyester B) and, if required, then applying further top coats.