The use of crosslinked copolymers obtainable by precipitation polymerization of monomer mixtures comprising (a) monoethylenically unsaturated C3-C8-carboxylic acids, their anhydrides or mixtures of said carboxylic acids and anhydrides, (b) compounds with at least 2 non-conjugated ethylenic double bonds in the molecule as crosslinkers and, where appropriate, (c) other monoethylenically unsaturated monomers which are copolymerizable with monomers (a) and (b), in the presence of free-radical polymerization initiators and from 0.1 to 20% by weight, based on the monomers used, of saturated, nonionic surface-active compounds, as stabilizer in oil-in-water emulsions in amounts of from 0.01 to 5% of the weight of the emulsions, and cosmetic and pharmaceutical formulations based on oil-in-water emulsions which contain said precipitation polymers.