PURPOSE: To exactly detect the time for deterioration of a catalyst by detecting the point of the time when the difference in the max. values of the respective output voltages of oxygen sensors respectively disposed on the upper stream and down stream of the catalyst falls below a prescribed value.

CONSTITUTION: The oxygen sensors 4, 5 are respectively disposed on an exhaust passage 2 on the upper stream and down stream of the ternary catalyst 3 disposed in the exhaust passage of an internal combustion engine 1. The sensors 4, 5 are respectively electrically connected to an electronic control device 6. The device 6 controls a fuel injection valve 8 according to the output from the sensor 4. Since the output voltage of the sensor 5 changes according to the deterioration condition of the catalyst 3, the difference between the max. value of the output from the sensor 4 and the max. value of the output from the sensor 5 decreases according to the deterioration condition of the catalyst 3. The value of the above-mentioned difference corresponding to the time for exchanging the catalyst 3 is, therefore, previously set and the above-mentioned difference is monitored in the device 6, by which the deterioration of the catalyst is decided.