The present invention relates to a multistage process in which a series of components which each have surfaces of steel are initially provided with a conversion layer based on Zr and/or Ti and are subsequently dip-coated, wherein the conversion treatment stage is followed by a rinsing stage in which at least the surfaces of steel of each component are contacted with an aqueous composition containing hydrogen peroxide and the process provides excellent corrosion protection on steel surfaces even under unfavorable process conditions which promote corrosion defects on steel surfaces and have a negative effect overall on corrosion protection.