A gear-change device for a motor vehicle, comprising: - at least one primary shaft, which can be connected to the crankshaft of the motor vehicle by means of a clutch device; - at least one secondary shaft, the axis of which is parallel to and set at a distance from the axis of said primary shaft, and which bears an output pinion that is to mesh with a gear of a differential; - a plurality of pairs of gears (IA, IB; IIA, IIB; IIIA, IIIB; IVE, IVB; VA; VB; VIA, VIB) corresponding to a plurality of forward-gear ratios (I, II, III, IV, V, VI), in which the gears of each pair are one that is rigidly connected in rotation to one of said primary and secondary shafts (3, 6) and the other that is freely rotatable with respect to the other of said primary and secondary shafts (3, 6); - a plurality of gear-selection devices (S1/2, S3/4, S5/6) for coupling in rotation each of said freely rotatable gears with the shaft on which it is mounted; and - a reverse gear mounted freely rotatable on a third shaft, the axis of which is set at a distance both from the axis of said primary shaft and from the axis of said secondary shaft, said reverse gear being connectable in rotation to said third shaft by means of a reverse-gear selection device, - said reverse gear always meshing with a gear mounted freely rotatable on the secondary shaft forming part of one of said pairs of forward gears (IA, IB), - wherein said third shaft is connected via a gear reducer to the shaft of an electrical machine associated to said gear-change device and designed to operate both as electric motor and as electric generator and having a casing rigidly connected to the casing of said gear-change device, - said gear-change device being moreover characterized in that said third shaft carries a second output pinion that is also designed to mesh directly with the aforesaid gear of the differential, wherein said gear reducer comprises a pair of gears (16, 17), including a first gear carried by the shaft of the electrical machine and a second gear meshing with said first gear carried by the shaft of the electrical machine and connected in rotation to said third shaft, said third shaft and the shaft of the electrical machine having their axes (9a, 11 a) set parallel to and at a distance from one another, characterized in that said second gear is a ring gear having an internal toothing meshing with said first gear, said internal toothing being made on a bell-shaped element connected in rotation to said third shaft. - at least one primary shaft, which can be connected to the crankshaft of the motor vehicle by means of a clutch device; - at least one secondary shaft, the axis of which is parallel to and set at a distance from the axis of said primary shaft, and which bears an output pinion that is to mesh with a gear of a differential; - a plurality of pairs of gears (IA, IB; IIA, IIB; IIIA, IIIB; IVE, IVB; VA; VB; VIA, VIB) corresponding to a plurality of forward-gear ratios (I, II, III, IV, V, VI), in which the gears of each pair are one that is rigidly connected in rotation to one of said primary and secondary shafts (3, 6) and the other that is freely rotatable with respect to the other of said primary and secondary shafts (3, 6); - a plurality of gear-selection devices (S1/2, S3/4, S5/6) for coupling in rotation each of said freely rotatable gears with the shaft on which it is mounted; and - a reverse gear mounted freely rotatable on a third shaft, the axis of which is set at a distance both from the axis of said primary shaft and from the axis of said secondary shaft, said reverse gear being connectable in rotation to said third shaft by means of a reverse-gear selection device, - said reverse gear always meshing with a gear mounted freely rotatable on the secondary shaft forming part of one of said pairs of forward gears (IA, IB), - wherein said third shaft is connected via a gear reducer to the shaft of an electrical machine associated to said gear-change device and designed to operate both as electric motor and as electric generator and having a casing rigidly connected to the casing of said gear-change device, - said gear-change device being moreover characterized in that said third shaft carries a second output pinion that is also designed to mesh directly with the aforesaid gear of the differential,