During deterioration detection of a catalyst, exhaust gas of a lean air/fuel ratio and exhaust gas of a rich air/fuel ratio are alternately supplied to the catalyst, and decrease of the O2 storage function is detected by obtaining the oxygen occlusion amount in the catalyst, based upon the timing at which, after changeover of the air/fuel ratio of the exhaust gas flowing into the catalyst, the air/fuel ratio of the exhaust gas passed through the catalyst changes to track that air/fuel ratio of the exhaust gas flowing into the catalyst. At this time, the rich air/fuel ratio of the exhaust gas and the lean air/fuel ratio of the exhaust gas supplied to the catalyst are set closer to the stoichiometric air/fuel ratio, the larger is the exhaust flow amount.