The invention concerns a process for coating a metallic surface with an aqueous composition, wherein in addition to water the composition contains a) as the main component, an organic film former consisting of at least one synthetic resin, 70 to 100 wt. % of the content of synthetic resin(s) in the organic film former comprising at least one water-soluble or/and water-dispersible synthetic resin in the form of polymers, copolymers, block copolymers or/and graft copolymers based on synthetic resins selected from the group consisting of polycarbonate, polyurethane, ionomer, poly(meth)acrylate, polyester, polyether or/and polystyrene, the content of polycarbonate and polyurethane being at least 10 wt. % each, b) at least one long-chain alcohol as film-forming aid for the organic film former, c) at least one crosslinker, d) at least one lubricant, and e) at least one substance based on silane, silanol or/and siloxane or/and at least one inorganic compound in particle form with an average particle diameter measured on a scanning electron microscope in the range from 0.005 to 0.3 μm, and f) optionally at least one organic corrosion inhibitor, at least one organic solvent or/and at least one additive, wherein the metallic surface is brought into contact with the aqueous composition and a polymeric film is formed on the metallic surface with a film thickness in the range from 0.01 to 10 μm. The invention also concerns a corresponding aqueous composition.