Abstract: A transmission system includes an electrical power unit having a rotor mounted on a shaft which rotates at a predetermined speed and a stator defining a gap with the rotor, and a step-down speed-reducing unit. The speed-reducing unit includes a flexible sleeve extending through the gap and having adjacent one axial end of the rotor a first set of teeth, an eccentric element mounted on the shaft axially adjacent the rotor for rotation within the sleeve so as to impart the eccentricity of the eccentric element to the flexible sleeve as the shaft rotates, and an annular member having a second set of teeth which mesh with the first set, the numbers of teeth in the two sets being different from one another.