A method for passivating metallic surfaces, more particularly those of strip metals, by treating the surface in alternating layers with a) an acidic, aqueous preparation comprising at least one water-soluble copolymer (A) containing acid groups and b) an aqueous preparation comprising at least one water-soluble and/or water-dispersible species (B) which contains cationic and/or procationic groups, preferably a cationic and/or procationic polymer (B1), the preparation a) always being the first and the last layer.