A crystalline rare-earth oxide or sulfide which has an average particle diameter of 10 nm or less and in which the rare-earth element has a low valance, in particular, crystalline EuO or EuS of nano size. The rare-earth oxide or sulfide is produced by irradiating an inorganic acid salt or organic acid salt of a rare-earth element having a high valence with a light in the range of from UV to visible light in the presence of: a compound which, upon irradiation with the light in the range of from UV to visible light induces a photooxidation-reduction reaction and simultaneously converts the rare-earth ions having a high valence into ions having a low valence; and a cholagen source compound which immediately reacts with the low valence ions to form a cholagen compound.