Suspensions of cerium oxide particles, well suited for polishing applications, the particles (secondary particles) of which have an average size of at most 200 nm, these secondary particles are formed from primary particles whose average size measured by TEM is at most 150 nm with a standard deviation of at most 30% of the value of this average size, and for which the ratio of the average size measured by TEM to the average size measured by BET is at least 1.5. Such suspensions are prepared from solutions of a cerium III salt, comprising a colloidal dispersion of cerium IV, which are contacted, in the presence of nitrate ions and under an inert atmosphere, with a base, and the medium obtained is subjected to a thermal treatment under an inert atmosphere and then acidified and washed.