An aqueous dispersion of water-soluble and/or water-swellable anionic polymers which are obtainable by free radical polymerization of ethylenically unsaturated, anionic monomers in an aqueous medium in the presence of at least one stabilizer, the polymerization being carried out in the presence of at least one water-soluble polymer of the groups consisting of (a) graft polymers of vinyl acetate and/or vinyl propionate on (i) polyethylene glycols or (ii) polyethylene glycols or polypropylene glycols endcapped at one or both ends with alkyl, carboxyl or amino groups, polyalkylene glycols, polyalkylene glycols endcapped at one or both ends with alkyl, carboxyl or amino groups and (b) water-soluble copolymers from the group consisting of homo- and copolymers of anionic monomers, copolymers of anionic and cationic and, if appropriate, neutral monomers, the proportion of the anionic monomers incorporated in the form of polymerized units being greater than that of cationic monomers and copolymers of at least one anionic monomer and at least one monomer from the group consisting of the esters of anionic monomers with monohydric alcohols, styrene, N-vinylpyrrolidone, N-vinylcaprolactam, N-vinylimidazole, N-vinylformamide, acrylamide, methacrylamide, vinyl acetate and vinyl propionate as a stabilizer, processes for the preparation of the aqueous dispersions by free radical polymerization of ethylenically unsaturated, anionic monomers in an aqueous medium in the presence of a stabilizer of the abovementioned groups (a) and (b) and use of the aqueous dispersions as thickeners for paper coating slips, pigment print pastes, print pastes for transfer printing, dispersion printing, printing with acid and metal complex dyes, reactive printing and vat printing, for tertiary mineral oil production, for consolidating nonwovens, for water-based paints, pharmaceutical products, dental compounds, agrochemicals and extinguishing agents and as coating materials and as an additive in deterge
