An acidic preparation for passivating metallic surfaces with a pH ≤ 5, comprising at least water and also 0.1 to 50% by weight, based on the amount of all components of the preparation, of at least one water-soluble or water-dispersible copolymer comprising phosphoric and/or phosphonic acid groups, wherein the copolymer is composed of the following monomeric units: 15 to 80% by weight of at least one mono(meth)acrylic ester of the general formula H 2 C=CHR 1 -COOR 2, R 1 being H or methyl and R 2 being a radical selected from the following group: (R 2a) radicals of the general formula - (R 3 -O-) n -R 4, n being a natural number from 2 to 40, R 3 independently at each occurrence being a divalent, linear or branched alkyl radical having 2 to 4 C atoms, and R 4 being H or a linear or branched alkyl radical having 1 to 6 C atoms, (R 2b) radicals of the general formula -R 5 -X m, R 5 being an (m+1)-valent, linear or branched alkyl radical having 1 to 10 C atoms, X being a functional group selected from the group of -OH, -OR 6, -NH 2, -NHR 6, -NR 2 6,-N + HR 2 Y- or -N + R 3 Y -, R 6 being methyl or ethyl, Y being a monovalent anion, and m being a natural number from 1 to 6, with the proviso that there is not more than one functional group X per C atom in R 5, (R 2c) a mono- or oligosaccharide radical, 10 to 75% by weight of at least one monoethylenically unsaturated monomer which comprises phosphoric and/or phosphonic acid groups and/or salts and/or esters thereof, 5 to 70% by weight of at least one monoethylenically unsaturated monomer which comprises at least one COOH group and/or salts thereof, and 0 to 20% by weight of further ethylenically unsaturated monomers differing from to, wherein except for the monomers,, and if appropriate there are no monomers present. 15 to 80% by weight of at least one mono(meth)acrylic ester of the general formula H 2 C=CHR 1 -COOR 2, R 1 being H or methyl and R 2 being a radical selected from the following group: (R 2a) radicals of the general formula - (R 3 -O-) n -R 4, n being a natural number from 2 to 40, R 3 independently at each occurrence being a divalent, linear or branched alkyl radical having 2 to 4 C atoms, and R 4 being H or a linear or branched alkyl radical having 1 to 6 C atoms, (R 2b) radicals of the general formula -R 5 -X m, R 5 being an (m+1)-valent, linear or branched alkyl radical having 1 to 10 C atoms, X being a functional group selected from the group of -OH, -OR 6, -NH 2, -NHR 6, -NR 2 6,-N + HR 2 Y- or -N + R 3 Y -, R 6 being methyl or ethyl, Y being a monovalent anion, and m being a natural number from 1 to 6, with the proviso that there is not more than one functional group X per C atom in R 5, (R 2c) a mono- or oligosaccharide radical, (R 2a) radicals of the general formula - (R 3 -O-) n -R 4, n being a natural number from 2 to 40, R 3 independently at each occurrence being a divalent, linear or branched alkyl radical having 2 to 4 C atoms, and R 4 being H or a linear or branched alkyl radical having 1 to 6 C atoms, (R 2b) radicals of the general formula -R 5 -X m, R 5 being an (m+1)-valent, linear or branched alkyl radical having 1 to 10 C atoms, X being a functional group selected from the group of -OH, -OR 6, -NH 2, -NHR 6, -NR 2 6,-N + HR 2 Y- or -N + R 3 Y -, R 6 being methyl or ethyl, Y being a monovalent anion, and m being a natural number from 1 to 6, with the proviso that there is not more than one functional group X per C atom in R 5, (R 2c) a mono- or oligosaccharide radical, 10 to 75% by weight of at least one monoethylenically unsaturated monomer which comprises phosphoric and/or phosphonic acid groups and/or salts and/or esters thereof, 5 to 70% by weight of at least one monoethylenically unsaturated monomer which comprises at least one COOH group and/or salts thereof, and 0 to 20% by weight of further ethylenically unsaturated monomers differing from to,