An object of the invention is to provide a transmission device which has a simple structure and can be produced at a low cost. A second electromagnetic clutch is shut off at a timing when an electric motor is decelerated and before selecting motion is finished, and thereafter, a shift/select shaft is moved to a terminal end position of the selecting motion with an inertia of a driven part (a second output hub) of the second electromagnetic clutch. At a timing after a predetermined period has passed from the timing, a first electromagnetic clutch for the next shifting motion is connected. The electric motor is driven synchronously with the end of the selecting motion or immediately in response to the end, thereby to start the next shifting motion. In this manner, gear change can be rapidly conducted.