The invention relates to a multi-step method for the anti-corrosion pretreatment of components made from metallic material, in which following a wet-chemical treatment comprising an aqueous solution (A) containing a dissolved and/or dispersed polymer P, said polymer being substituted with heterocycles containing at least one quartenary nitrogen heteroatom, a conversion treatment based on aqueous compounds of the elements Zr, Ti and/or Si, is carried out, optionally prior to, additional coatings protecting against corrosion being applied.