A hybrid propulsion system for a motor vehicle includes a gearbox having a gear control device and first and second shafts. The gear control device includes a first drum control device associated with the first shaft, a second drum control device associated with the second shaft and an actuation unit arranged to bring about rotation of the first and second drum control devices in a synchronized manner. The actuation unit includes a motor device, a first gear associated with the first drum control device, a second gear associated with the second drum control device, and an intermediate gear. Either of the first and second gears meshes with an output pinion of the motor device, while the intermediate gear meshes both with the first gear and with the second gear.