This invention provides apparatus for detecting abnormality of an oxygen sensor accurately and also apparatus for appropriately controlling the air/fuel ratio of air and fuel mixture when an oxygen sensor is abnormal. The apparatus easily and properly detects a deteriorating oxygen sensor, with the use of which exhaust of nitrogen oxides or carbon monoxide increases, and when the oxygen sensor is determined to deteriorate, the feed back control of the air/fuel ratio of air and fuel mixture supplied to an internal combustion engine is preferably performed.