In a control device for an internal combustion engine provided with a NOX catalytic converter in an exhaust passage thereof, the progress of sulfur purging is computed from the consumption of reducing agent contained in the exhaust gas in the NOX catalytic converter. This computation may be based on the air fuel ratio of exhaust gas upstream of the NOX catalytic converter and the estimated consumption of the reducing agent contained in the exhaust gas or on the difference between the air fuel ratios of exhaust gas upstream and downstream of the NOX catalytic converter. In either case, the accuracy can be improved by taking into account the space velocity of the exhaust gas.