A transmission system for a motor vehicle includes two input shafts (11, 12), a mainshaft (15), an output shaft (5), a clutch arrangement (40) for connecting alternately the input shafts (11, 12), to a driveshaft, a first power transmission shaft (A1) provided with at least a first gearwheel (K1b) which is in engagement with a gearwheel (K17a) situated on either of the input shafts, and a second gearwheel (K3a) which is in engagement with a gearwheel (35b) situated on the mainshaft, and a second power transmission shaft (A1) provided with at least a first gearwheel (K4b) which is in engagement with a gearwheel (K4a) situated on either of the input shafts, and a second gearwheel (K5a) which is connected or connectable to the gearwheel (K35b) on the mainshaft via an intermediate gearwheel (K5c) to allow the establishment of a power transfer path for a reverse gear via these gearwheels (K5a, K5c, K35b).