A device for detecting deterioration of a NO x absorbent arranged in the exhaust passage of an engine. An O 2 sensor generating a current proportional to the air-fuel ratio is arranged in the exhaust passage downstream of the NO x absorbent. When the amount of NO x absorbed in the NO x absorbent is almost zero or after the amount of NO x absorbed in the NO x 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 NO x absorbent is detected from the output signal of the O 2 sensor at this time. Further, the NO x absorbing capability is found by using this detected oxygen amount.