Abstract: The transmission device (1) comprises two power paths (8a, 8b) mounted in parallel, permanently connected to the upper shaft (2) of the engine (3) and the lower shaft (4) to control the differential (6). In each path (8a, 8b), each gear ratio Ia, IIa, IIIa or Ib, IIb, IIIb is obtained by activating a single activator capable of adapting the rotating speed between the two shafts 2 and 4 during gear ratio changes. A control device (17) synchronises the activations/deactivations during gear ratio changes, whether the newly activated gear ratio is in the same path or a different path.