Cerium oxide powder having carbonate groups and made of crystalline primary particles containing cerium oxide and having carbonate groups on the surface and in a region close to the surface, and having a BET surface area of from 25 to 150 m.sup.2/g, a mean diameter of from 5 to 50 nm, a carbonate concentration in the region close to the surface decreasing inwardly from the surface, a carbon content due to carbonate groups on the surface of from 5 to 50% by area, a carbon content due to carbonate groups at a depth of about 5 nm in a region close to the surface of from 0 to 30% by area, a content of cerium oxide calculated as CeO.sub.2 and based on the powder of at least 99.5% by weight and a content of organic and inorganic carbon of from 0.01 to 0.3% by weight. A dispersion containing this powder.