FIELD: chemical or physical processes. SUBSTANCE: invention relates to the technology of producing compositions based on zirconium oxide and cerium oxide with the addition of at least one rare-earth element and can be used in automotive transport exhaust gases neutralization systems. Method includes preparation in a liquid medium of a mixture containing a compound of zirconium, cerium, lanthanum and another rare-earth element; mixing said mixture with a basic compound to obtain a precipitate; heating said precipitate in a liquid medium to a temperature of at least 100 °C; addition to additive obtained at previous stage, additive, selected from anionic surfactants, nonionic surfactants, polyethylene glycols, carboxylic acids, and salts, and surfactants thereof, such as carboxy methylated fatty alcohol ethoxylates; drying and annealing the residue, wherein preparation in a liquid medium of the mixture is carried out by preparing a solution of zirconium nitrate or chloride by dissolving basic zirconium carbonate in nitric or hydrochloric acid at molar ratio of corresponding acid to zirconium in range from 1 to 1.4 with subsequent heating of solution of nitrate or zirconium chloride to temperature of not less than 60 °C to obtain solution I; preparing solution II, containing water-soluble salts of cerium, one or more other rare-earth elements and water; preparing the mixture by mixing solution I and solution II; mixing is performed by dosing mixture into reaction volume, in which mixing and constant pH is maintained from range of values from 7 to 9 inclusive, due to controlled introduction of aqueous solution of ammonia; after mixing precipitation is dispersed to obtain a suspension with mean particle diameter of not more than 10 mcm inclusive. EFFECT: technical result consists in increase of specific surface area of system based on oxides of zirconium and cerium due to change of technology of preparation in liquid medium of mixture, containing compounds of zirconium, cerium, lanthanum and other rare-earth element, change of mixing of said mixture with main compound to obtain a precipitate, as well as by introducing an additional step of dispersing the precipitate to obtain a suspension with an average particle diameter of at least 10 mcm, inclusive.