A control apparatus for an internal combustion engine can effectively suppress the rotational fluctuation of the engine by properly controlling the operating state of a rotating electrical machine without applying an excessive load to a power supply system connected to the rotating electrical machine. The rotating electrical machine is used for both electric operation and electric power generation, and is connected to the engine. A control circuit controls at least one of a field current and an armature current of the rotating electrical machine. A power supply system is connected to the rotating electrical machine. A rotational fluctuation suppression section (ECU) suppresses the rotational fluctuation of the engine by controlling an amount of electric power and generated torque of the rotating electrical machine in accordance with an electric power load of the vehicle, an amount of electric power of the power supply system, and the rotational speed of the rotating electrical machine.