The present invention relates to surface-modified nanoparticulate metal oxides where the metal is chosen from the group consisting of aluminum, cerium, iron, titanium, zinc and zirconium, wherein the surface modification comprises a coating with a copolymer P comprising, as monomers, A) 1 to 99 mol % of a N-vinylamide N-vinylpyrrolidone and B) 99 to 1 mol % of a monomer comprising, per molecule, a free-radically polymerizable .alpha.,.beta.-ethylenically unsaturated double bond and an anionogenic and/or anionic group, with the proviso that the copolymer P must comprise no further monomers chosen from the group consisting of C.sub.8-C.sub.30-alkyl esters of monoethylenically unsaturated C.sub.3-C.sub.8-carboxylic acids, N-alkyl- or N,N-dialkyl-substituted amides of acrylic acid or of methacrylic acid with C.sub.8-C.sub.18-alkyl radicals, or vinyl esters of aliphatic C.sub.8-C.sub.30-carboxylic acids.