A particulate filter is provided in an exhaust system of the engine. Parameter values correlated with a flow amount of exhaust gas of the engine are determined, and differential pressure between upstream and downstream sides of the particulate filter is determined. The ratio of a variation rate of the parameter values correlated with the exhaust flow amount to a variation rate of the differential pressure is compared with a predetermined threshold value during transitional operation of the engine to determine the state of the particulate filter.