The invention relates to an aqueous coating material for metallic substrates, comprising a water-dispersible and/or water-soluble polymer P with a gradient in the concentration of covalently bonded hydrophilic groups along the main polymer chain, the polymer P having covalently bonded ligands A, which form chelates with the metal ions released during the corrosion of the substrate and/or with the substrate surface, and having crosslinking functional groups B, which with themselves, with further complementary functional groups B′ of the polymer P and/or with further functional groups B and/or B′ are able to form covalent bonds to crosslinkers V.