An aqueous dispersion with a pH of from 2 to 7, comprising (A) at least one swellable polymer or oligomer containing anionic and/or potentially anionic functional groups, (B) surface-modified, cationically stabilized, inorganic nanoparticles of at least one kind, and (C) at least one amphiphile; and its use for producing highly scratch-resistant coatings, moldings, and self-supporting films.