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Disclosed are : a complex oxide which has excellent heat resistance and excellent catalytic activity and is capable of maintaining high pore volume even if used in a high temperature environment; a method for producing the complex oxide; and an exhaust gas purifying catalyst which uses the complex oxide. Specifically disclosed is a complex oxide which contains cerium and at least one element selected from aluminum, silicon and rare earth metals including yttrium but not including cerium, at a mass ratio within the range from 85 : 15 to 99 : 1 in terms of oxides. The complex oxide has physical properties such that the volume of pores having a pore diameter of 200 nm or less after 5-hour firing at 900°C is not less than 0.30 cm3/g, preferably not less than 0.40 cm3/g. In particular, the complex oxide is suitable as a promoter for an exhaust gas purifying catalyst that is used in an automobile or the like.