The present invention relates to an aqueous composition and to a method for the anticorrosion conversion treatment of metallic surfaces, particularly metallic materials which are assembled into composite structures, comprising steel or galvanized or alloy-galvanized steel and any combinations of these materials, the composite structure being composed at least in part of aluminum or the alloys thereof. The aqueous composition according to the invention is based on a phosphating solution and contains, in addition to water-soluble compounds of zirconium and titanium, a quantity of free fluoride in a ratio that both permits phosphating of the steel and galvanized and/or alloy-galvanized steel surfaces and determines low pickling rates with regard to the aluminum substrate with simultaneous passivation of the aluminum. The metallic materials, components and composite structures conversion treated in accordance with the underlying invention are used in automotive body construction, in shipbuilding, in construction and for the production of white goods.