A target air-fuel ratio KCMD for an exhaust gas upstream of a catalytic converter is sequentially determined to converge the output V02/OUT of an 02 sensor downstream of the catalytic converter to a target value V02/TARGET, and the amount of fuel supplied to an internal combustion engine is controlled to converge the output KACT of an air-fuel ratio sensor to the target air-fuel ratio KCMD. While the amount of fuel supplied to the internal combustion engine is being thus controlled, the value of a deterioration linear function sigma whose variable components are represented by time-series data of the output V02/OUT of the 02 sensor is determined. A central value of the square sigma <2> of the value of the deterioration linear function sigma is determined as a deterioration evaluating parameter. A deteriorated state of the catalytic converter is evaluated on the basis of the value of the deterioration evaluating parameter. |