PURPOSE: To improve diagnostic precision by providing sensors for outputting signals according to exhaust air-fuel ratio on the upstream and downstream sides from the catalytic converter of an exhaust passage, and diagnosing the abnormality of a variable dynamic valve device on the basis of the sensor output on the downstream side.

CONSTITUTION: In an engine having a variable dynamic valve device 22 for adjusting the valve lift characteristic according to the operating state, the air- fuel ratio is controlled, when the exhausting NOx to a catalytic converted is increased, so as to be close to a target value on the basis of the output of a sensor 23 interposed on the upstream side from the catalytic converter to reduce the NOx by the catalytic converter. Then, the output of a sensor 25 on the downstream side from the catalytic converter is changed to lean side. In a valve lift characteristic diagnostic means 26, it is diagnosed on the basis of the output of the sensor 25 whether the valve overlap quantity of suction and exhaust valves is properly provided by the operation of the variable dynamic valve device 22 from the exhausting NOx concentration.