The invention relates to the use of an apparatus for adding at least one solid or viscous liquid additive, or an additive dispersed in solvent, to a reactor interior of a reactor for preparing crosslinked, finely divided polymers by copolymerizing (a) water-soluble, monoethylenically unsaturated monomers and (b) from 0.001 to 5 mol %, based on the monomers (a), of monomers comprising at least two polymerizable groups, (c) from 0 to 20 mol %, based on the monomers (a), of water-insoluble monoethylenically unsaturated monomers, where the apparatus comprises at least one screw for conveying the at least one additive and the at least one screw ends in an addition orifice substantially flush with the inner wall of the reactor interior.