On the basis of absolute values α and β of variations, before and after actuation of an exhaust brake, of fuel-injection and intake-air amounts, respectively, an exhaust brake is determined to normally operate when the absolute values α and β of the variations of the fuel-injection and intake-air amounts are not less than fuel-injection and intake-air variation thresholds, respectively; the exhaust brake is determined to have failure when the absolute values α and β of the variations of the fuel-injection and intake-air amounts are less than the fuel-injection and intake-air variation thresholds, respectively.