This invention provides a method for preparing nanoparticles comprising cerium oxide and zirconium and having a narrow size distribution. The method comprises providing a first aqueous solution comprising zirconium oxychloride and providing a second aqueous solution comprising a first component which is either cerium nitrate or hexamethylenetetramine. The second aqueous solution is added to the first aqueous solution to form a first mixture. A third aqueous solution comprising a second component which is either cerium nitrate or hexamethylenetetramine, and which is different from the first component, is added to the first mixture to form a second mixture. The second mixture is maintained at a temperature no higher than about 320.degree. K. to form nanoparticles. The nanoparticles are then separated from the second mixture and sintered in air at a temperature ranging between about 500.degree. and about 1100.degree. C. The nanoparticles obtained by the method of the invention are at least in part crystalline.