A method for the anti-corrosion treatment of a plurality of metal surfaces of components in series that comprise zinc and/or iron, in which each of said components is brought into contact with a passivating aqueous pretreatment solution, located in a system tank, at a temperature of less than 50 °C, the passivating aqueous pretreatment solution containing one or more water-soluble compounds of the elements zirconium and/or titanium and one or more water-soluble compounds that are a source for fluoride ions, and being brought into contact for such a time that, on the metal surfaces of zinc and/or iron, a coating layer of at least 0.1 mmol/m 2 based on the elements zirconium and/or titanium is formed, although none of these metal surfaces comprises a coating layer of greater than 0.7 mmol/m 2 based on the elements zirconium and/or titanium, and, during the anti-corrosion treatment of the components in series, some of the passivating aqueous pretreatment solution in the system tank being rejected and replaced by a part by volume, which is in total at least the same size, of one or more additional solutions by metered addition into the system tank in such a way that the concentration of the elements zirconium and/or titanium in the passivating aqueous pretreatment solution is maintained in the form of water-soluble compounds, characterized in that a concentration of the elements zirconium and/or titanium in the passivating aqueous pretreatment solution is maintained in the form of water-soluble compounds of at least 0.05 mmol/L but of a total of less than 0.8 mmol/L in the system tank, and the molar ratio of the total amount of fluorine in the form of water-soluble compounds that are a source for fluoride ions to the total amount of the elements zirconium and/or titanium in the form of water-soluble compounds in the metered total volume of the additional solutions is less than the same ratio in the passivating aqueous pretreatment solution, but no less than 4.5, and the rejection of passivating aqueous pretreatment solution in liters per square meter of metal surfaces of zinc and iron treated in series assumes at least the following value: VW = z E − 2, 4 2, 8 mmol L − 1 − c B Me z E − 6 ⋅ 10 − 1 mmol m − 2 VW: rejection of pretreatment solution in L/m 2; c B Me: concentration of zirconium and/or titanium in the pretreatment solution in mmol/L; Z E: molar ratio of the total amount of fluorine in the form of water-soluble compounds that are a source for fluoride ions to the total amount of the elements zirconium and/or titanium in the form of water-soluble compounds in the metered total volume of the additional solutions with the proviso that the following applies: z E < 2, 8 mmol L − 1 c B Me + 6 VW: rejection of pretreatment solution in L/m 2; c B Me: concentration of zirconium and/or titanium in the pretreatment solution in mmol/L; Z E: molar ratio of the total amount of fluorine in the form of water-soluble compounds that are a source for fluoride ions to the total amount of the elements zirconium and/or titanium in the form of water-soluble compounds in the metered total volume of the additional solutions with the proviso that the following applies: z E < 2, 8 mmol L − 1 c B Me + 6