To enhance supercharge performance effectively and promote temperature rise of catalyst in cold time by using a plurality of exhaust gas turbochargers.

The engine is provided with the first and second exhaust gas turbochargers which are serially connected, catalysts connected to their downstream, a means for controlling a variable exhaust valve so as to reduce an effective opening area of an outlet of an independent exhaust passage in a predetermined supercharge operation area, a means for extending an overlap period of supply and exhaust valves in the predetermined supercharge operation area, a temperature state judging means, a turbine bypass passage for bypassing a turbine of the second turbo supercharger, an exhaust gas flow passage switch valve and a flow passage selecting means. The flow passage selecting means controls the exhaust gas flow passage switch valve so that exhaust gas flows to the catalyst through the turbine of the first exhaust turbo supercharger and the turbine bypass passage during cold time in the predetermined supercharge operation area and the exhaust gas flows through turbines of both the exhaust gas turbo superchargers during a warm time in the predetermined supercharge operation area.

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