A multi-cylinder engine comprising an intake manifold equipped with a carburetor. A secondary throttle valve is provided for each cylinder. Each of the secondary throttle valves is arranged in the respective manifold branch and fixed onto a common throttle shaft. An auxiliary intake passage is branched off from the collecting portion of the intake manifold and connected to a distribution channel. Each of the intake ports is connected to the distribution channel via a corresponding channel branch which opens into the intake port at a position near the intake valve. The common throttle shaft of the secondary throttle valves is connected to a vacuum operated diaphragm apparatus so that the secondary throttle valves are opened in accordance with a reduction in the level of vacuum produced in the intake manifold.