An internal combustion engine wherein exhaust gas from the cylinder groups (1, 2) is supplied to a common NOx storage catalyst (12). When the NOx storage catalyst (12) should release the SOx, the average air-fuel ratio of one cylinder group (1) is made rich and the average air-fuel ratio of the other cylinder group (2) is made lean. At this time, the air-fuel ratios of the cylinders (3) of one cylinder group (1) are made one target rich air-fuel ratio selected from two predetermined target rich air-fuel ratios, while the air-fuel ratios of the cylinders (3) of the other cylinder group (2) are made one target lean air-fuel ratio selected from two predetermined target lean air-fuel ratios.