A process for the anticorrosive treatment of metal components that have been heat-treated at a temperature of at least 100° C. and at least partially comprise zinc surfaces, wherein the surfaces of the component that consist of zinc already partially have a crystalline zinc phosphate layer, wherein the cleaned component is given an activating pretreatment with an acidic aqueous dispersion of insoluble phosphates having a pH of not less than 4 and the component is subsequently subjected to a phosphating conversion treatment before electrocoating is applied. The invention also comprises the use of metal components that have been treated in such a process, for the application of multilayer systems and in particular for the manufacture of bodies in automobile production.