An internal combustion engine including a first turbocharger operated at all intake air quantities and a second turbocharger operated only at large air intake air quantities, an intake switching valve located downstream of the compressor of the second turbocharger, an exhaust switching valve located downstream of the turbine of the second turbocharger, and an exhaust bypass valve for bypassing the exhaust switching valve. For the purpose of running-up the second turbocharger before the operation is changed from a "one-turbocharger-operation" to a "two-turbocharger-operation", the exhaust bypass valve is partially opened and then the amount by which the exhaust bypass valve is opened is gradually increased until it is fully opened so that any torque shock accompanying the operational change is effectively suppressed.