PURPOSE: To enlarge an output difference between both air-fuel ratio sensors and provide a stable judgement value by providing sensors at the upstream and downstream sides of a catalyst, and starting to make judgement about catalyst deterioration state via the comparison of output values from both sensors, when the output of the downstream sensor reaches the preset fuel-rich value.

CONSTITUTION: An exhaust manifold 13, a catalyst converter 14 and an exhaust pipe 15 are connected to an engine body 1, and oxygen sensors 16 and 17 (air- fuel ratio sensors) are laid both upstream and downstream of the converter 14. Also, output signals from the sensors 16 and 17, an air flow meter 8 or the like are inputted to a control unit 39, and when an output value from the downstream oxygen sensor 17 becomes equal to or more than the preset value in a fuel-rich condition, the upstream oxygen sensor 16 is judged to be normal. When a ratio of each accumulated value of the sensors 16 and 17 is less than a threshold value, the catalyst is judged to have deteriorated, thereby turning on an error lamp. In this way, judgement is started, when an output difference between both sensors 16 and 17 is sufficiently large, thereby preventing the occurrence of improper judgement.