Abstract: A composite oxide having oxygen absorbing and desorbing capability contains 4.99-98.89% by weight of cerium oxide, 1-95% by weight of zirconium oxide, 0.01-20% by weight of hafnium oxide, and 0.1-10% by weight of an additional metal oxide selected from titanium oxide, tungsten oxide, nickel oxide, copper oxide, iron oxide, aluminum oxide, silicon oxide, beryllium oxide, magnesium oxide, calcium oxide, strontium oxide, barium oxide, oxides of rare earth metals other than cerium, and mixtures thereof. The composite oxide includes .PHI. phase as a crystal phase, and has oxygen absorbing and desorbing capability of at least 100 .mu.mol/g at 400.degree.-700.degree. C. The composite oxide is prepared by the wet method or by the dry method.