The invention relates to a process for treating metal surfaces, preferably of aluminum, aluminum alloys and steel, for the subsequent application of organic coating compositions. The metal surfaces are wetted with an aqueous bath solution containing chromium(III)ions, fluoride ions and an organic film former which is soluble or homogeneously dispersible in water, after which the solution applied is dried and converted by heating into a water-insoluble film.The bath solution preferably contains the following constituents and approximate quantities thereof: 0.5 to 10 g/l of chromium(III)ions, 0.55 to 11 g/l of fluoride ions, 0.6 to 12.5 g/l of phosphate ions, and 0.15 to 5.0 g/l of organic film former. The organic film former preferably used is a polymer containing free carboxyl groups, more preferably a homopolymer and/or copolymer of acrylic and/or methacrylic acid.