The sulfur poisoning of a three-way catalyst is intended to be detected with a high degree of accuracy. It is determined whether the sulfur poisoning of the three-way catalyst is made to be recovered, or a determination is made that the degree of sulfur poisoning of the three-way catalyst is higher when the concentration of NOx detected by an NOx sensor is high than when it is low, based on the concentration of NOx downstream of the three-way catalyst after the air fuel ratio of the exhaust gas flowing into the three-way catalyst has been made to change from a rich air fuel ratio to a lean air fuel ratio and before the air fuel ratio of the exhaust gas flowing out of the three-way catalyst changes to a lean air fuel ratio.