Method for managing NOx catalyst

In a diesel engine, prior to a sulfur discharging process, a pre-process is performed to decrease the air-fuel ratio of the air-fuel mixture that is to be burned in the engine so that the air-fuel ratio A/FEHT of the exhaust gas reaches a predetermined pre-process value alpha . The time required for the air-fuel ratio A/FEHT of the exhaust gas to stabilize near the pre-process value alpha is set as a stand-by time TS. The sulfur discharging process starts after the stand-by time elapses. This enhances the convergence of the air-fuel ratio A/FEHT to the target value during the sulfur discharging process. If a predetermined condition is satisfied, the stand-by time is cancelled to start the sulfur discharging process when or just after the pre-process is started. This efficiently processes the sulfur components accumulated in a NOx storage catalyst, which is arranged in an exhaust passage of the engine, without deteriorating the exhaust gas property.