A composite oxide is provided which has large oxygen absorption and desorption over a wide temperature range, in particular in a higher temperature range of not lower than 700° C. and/or in a lower temperature range of not higher than 400° C. The composite oxide contains oxygen, R composed of at least one of Ce and Pr, and Zr at a particular ratio, and optionally a particular ratio of M composed of at least one element selected from alkaline earth metals and the like.