Surface-modified nanoparticles whose surface is covered completely or near-completely with(A) modifying groups which are attached covalently to the surface via linking functional groups (a) and contain inert spacer groups (b) and contain reactive functional groups (c) which are connected via the groups (b) to the groups (a) and are inert toward the reactive functional groups of the surface to be modified, (B) modifying groups which are attached covalently to the surface via linking functional groups (a) and contain inert groups (d) having a smaller hydrodynamic volume V.sub.H than the inert spacer groups (Ab), and (C) modifying groups which are attached to the surface via linking functional groups (a) which contain at least one silicon atom, contain inert groups (e), and have a smaller hydrodynamic volume V.sub.H than the modifying groups (A); dispersions comprising the nanoparticles, processes for preparing them, and their use.