Exhaust gas purifying apparatus for internal combustion engine

An exhaust gas purifying apparatus comprises a control unit (29) operative to estimate an amount of NOx absorbed by a NOx trap material (17) disposed in an exhaust passage (10) and to make an air-fuel ratio richer so as thereby to cause the NOx trap material to release sulfur when the estimated amount of NOx absorption exceeds a specified amount. Further, the control unit (29) operative to estimate an amount of sulfur absorbed by the NOx trap material (17) and to make an air-fuel ratio richer and rising a temperature of exhaust gas so as thereby to cause the NOx trap material to release sulfur when the estimated amount of sulfur absorption exceeds a specified amount. The control means restricts an air-fuel ratio from being made richer when the NOx trap material is not expected to absorb NOx due to progress of sulfur absorption resulting from conditionally the sulfur releasing.