Metal surfaces are treated with acidic aqueous compositions to form conversion coatings. The acidic aqueous compositions contain fluorometallate anions, divalent and/or trivalent cations of certain elements such as zinc, phosphorus-containing inorganic oxyanions, phosphonate anions containing phosphorus atoms directly bonded to carbon atoms, and water-soluble and/or water-dispersible organic polymers and/or polymer-forming resins.