The degree of deterioration of a catalyst is obtained accurately in cases where a plurality of catalysts is disposed at an exhaust passage of an internal combustion engine. Under the assumption that the degree of deterioration of a catalyst which is disposed at a location upstream of an NOx selective reduction catalyst and has an oxidizing ability is at a predetermined value, the ratio of NO2 in the NOx which inflows into the NOx selective reduction catalyst is estimated; the NOx removal rate of the NOx selective reduction catalyst is calculated a plurality of times at least until a local maximum value is obtained; and the degree of deterioration of the catalyst having an oxidizing ability is determined by comparison between the ratio of NO2 observed when the NOx removal rate of the NOx selective reduction catalyst reaches the local maximum value and a reference value of the ratio.