Driving force transmitting apparatus

A driving force transmitting apparatus includes: a first torque-transmitting member having a cylindrical portion and provided with a spline tooth; a second torque-transmitting member positioned inside the cylindrical portion and arranged coaxially rotatably relative to the first torque-transmitting member; a main clutch with a spline tooth; an actuator unit for actuating the main clutch to be engaged; and a controlling device for controlling the actuator unit so as to pressurize the main clutch plate in such a manner that torque is not substantially transmitted between the first torque-transmitting member and the second torque-transmitting member when the engagement of the main clutch is judged to be unnecessary.