of the exhaust gas from the engine is forced to flow in the main exhaust system thus in this case the auxiliary catalytic converter 18 is free of a thermal degradation furthermore since the bypass exhaust passage is opened but in a small degree a part of the exhaust gas is permitted to enter the bypass exhaust passage when under a high speed and high load operation condition a larger amount of exhaust gas is produced by the engine this prevents lowering of charging efficiency of the cylinders caused by a back pressure as is described hereinabove the main exhaust passage system is in the form of u201c 4 2 1 u201d united type arrangement and thus increase in the charging efficiency of the cylinders is achieved with the aid of the exhaust dynamic effect while the bypass exhaust passage system is arranged in the above mentioned manner without taking the exhaust interference avoidance into a consideration however since each upstream bypass exhaust passage 11 used has a sufficiently smaller cross sectional area the exhaust interference inevitably induced by a communication with the corresponding cylinder can be reduced to a very small degree if the cross sectional area of upstream bypass exhaust passage 11 is made larger than a predetermined high degree a marked lowering of the charting efficiency would take place due to the exhaust interference while if the cross sectional area is made smaller than a predetermined low degree the amount of exhaust gas during the time when switch valves 4 a and 4 b are kept in their closed position is excessively reduced and thus the.