An exhaust purification device which is capable of detecting the degree of deterioration of the NOx absorbent or the three-way catalyst arranged in the exhaust passage of an engine. An O.sub.2 sensor whose output current or output voltage is proportional to the air-fuel ratio is arranged inside the exhaust passage downstream of the NOx absorbent or three-way catalyst. The air-fuel ratio of the air-fuel mixture is temporarily changed from lean to rich or from rich to lean to enable the degree of deterioration of the NOx absorbent or three-way catalyst to be detected from the peak value of the output current or voltage of the O.sub.2 sensor during the time when the air-fuel ratio is changed.