To diagnose deterioration of an exhaust gas emission control device with high accuracy by estimating a temperature of an absorbing catalyst outlet from an operating condition of an internal combustion engine and an exhaust gas temperature of an absorbing catalyst inlet, and judging a deteriorating condition of a hydrocarbon absorbing catalyst from a temperature difference between the estimated outlet exhaust temperature and detected outlet exhaust temperature.

At the time of engine operation, it is judged in an ECU 4 whether a cooling water temperature is a prescribed temperature or more or not, and deterioration is diagnosed when a water temperature is a prescribed temperature and less and cooling is started. An operating condition of the engine is judged from an intake air rate of an engine, a throttle opening, and traveling speed, and a HC absorbing catalyst outlet exhaust temperature Tc is found out of its judged operating condition and a HC absorbing catalyst inlet exhaust temperature. A temperature difference between the outlet exhaust temperature Tc and a real outlet exhaust temperature Tco is found out, and a deteriorating condition of an absorbing catalyst 3 is judged. When, namely a temperature difference between an inlet exhaust temperature and the outlet exhaust temperature Tc is larger than a temperature difference between the real inlet exhaust temperature and the outlet exhaust temperature Tco, deterioration is not judged.