A device for detecting deterioration of a NOx absorbent arranged in the exhaust passage of an engine. An O2 sensor generating a current proportional to the air-fuel ratio is arranged in the exhaust passage downstream of the NOx absorbent. When the amount of NOx absorbed in the NOx absorbent is almost zero or after the amount of NOx absorbed in the NOx absorbent is made almost zero, the air-fuel ratio of the air-fuel mixture is changed from lean to rich, and the amount of oxygen stored in the NOx absorbent is detected from the output signal of the O2 sensor at this time. Further, the NOx absorbing capability is found by using this detected oxygen amount.