Abstract: A method for coating a metallic surface by contacting it with an aqueous copolymer dispersion, wherein the aqueous copolymer dispersion comprises an effective amount of organic phosphorus-containing corrosion inhibitors, the copolymers present in the dispersion being constructed from 20 to 95 weight % of monoethylenically unsaturated hydrocarbons and/or hydrocarbons having two conjugated double bonds, from 5 to 80 weight % of monoethylenically unsaturated monomers which contain acid groups, and/or anhydrides or salts thereof. A metallic surface coated with a copolymer, obtainable by methods of this kind, which can also further comprise one or more layers of paint applied one atop another.