A composite oxide having oxygen absorbing and desorbing capability contains 4.99-98.99% by weight of cerium oxide, 1-95% by weight of zirconium oxide and 0.01-20% by weight of hafnium oxide. 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. to 700.degree. C.