The present invention relates to an acidic aqueous composition for coating metallic surfaces, particularly of aluminium materials, that comprises, besides water and optionally further components, a) at least one compound selected from the group consisting of organoalkoxysilanes, organosilanols, polyorganosilanols, organosiloxanes and polyorganosiloxanes, b) at least one compound selected from the group consisting of titanium, zirconium, hafnium and aluminium compounds and silicon complex fluoride, and c) at least one copolymer which is stable at least in a segment of the pH range below 6 and which comprises, in alternating configuration, monomer units containing at least one carboxylic and/or phosphonic acid group and monomer units containing no acid group. The invention further relates to a corresponding coating method and to the use of the substrates coated by this method.