A hybrid powertrain unit for a motor vehicle, comprising: - an internal-combustion engine; and - a gearbox device including: - at least one primary shaft, that can be connected to the crankshaft of the internal combustion engine by means of a clutch device, - at least one secondary shaft, the axis of which is parallel to, and spaced apart from, the axis of said primary shaft and which carries an output pinion; - a plurality of pairs of gears (I1, 12, II1, II2, III1, III2, IV1, IV2, V1, V2, VI1, VI2) corresponding to a plurality of forward gear ratios (I, II, III, IV, V, VI), in which the gears of each pair are one rigidly connected in rotation with respect to one of said primary and secondary shafts (3, 7) and the other freely rotatable with respect to the other of said primary and secondary shafts; and - 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, said unit further comprising: - a differential, having a first crown wheel meshing with said output pinion of said secondary shaft of the gearbox device; - an electric machine adapted to operate both as electric motor and as electric generator and having a casing rigidly connected to a supporting structure of said powertrain unit, and a shaft connected by means of a connecting transmission to a second crown wheel of said differential; - an engagement device arranged, in said connecting transmission, between the shaft of the electric machine and the aforesaid second crown wheel of the differential; and - means for actuating said engagement device, said powertrain unit being characterized in that said connecting transmission includes an auxiliary shift device configured for providing at least two different selectable transmission ratios, and in that said auxiliary shift device comprises an epicyclic gear train, including: - a sun gear, an outer ring gear, a plurality of planet gears meshing around the sun gear and within the outer ring gear, and a planet carrier carrying the planet gears, - said sun gear being connectable in rotation with said second crown wheel of the differential, - said planet carrier being connected to the shaft of said electric machine, and - said outer ring gear being axially movable between a first operating position in which it is connected in rotation with the planet carrier and a second operating position in which it is blocked on the supporting structure of the unit; and - a device for selection of the transmission ratio for displacing selectively the aforesaid outer ring gear between its two operating positions. - an internal-combustion engine; and - a gearbox device including: - at least one primary shaft, that can be connected to the crankshaft of the internal combustion engine by means of a clutch device, - at least one secondary shaft, the axis of which is parallel to, and spaced apart from, the axis of said primary shaft and which carries an output pinion; - a plurality of pairs of gears (I1, 12, II1, II2, III1, III2, IV1, IV2, V1, V2, VI1, VI2) corresponding to a plurality of forward gear ratios (I, II, III, IV, V, VI), in which the gears of each pair are one rigidly connected in rotation with respect to one of said primary and secondary shafts (3, 7) and the other freely rotatable with respect to the other of said primary and secondary shafts; and - 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, said unit further comprising: - a differential, having a first crown wheel meshing with said output pinion of said secondary shaft of the gearbox device; - an electric machine adapted to operate both as electric motor and as electric generator and having a casing rigidly connected to a supporting structure of said powertrain unit, and a shaft connected by means of a connecting transmission to a second crown wheel of said differential; - an engagement device arranged, in said connecting transmission, between the shaft of the electric machine and the aforesaid second crown wheel of the differential; and - means for actuating said engagement device, - a sun gear, an outer ring gear, a plurality of planet gears meshing around the sun gear and within the outer ring gear, and a planet carrier carrying the planet gears, - said sun gear being connectable in rotation with said second crown wheel of the differential, - said planet carrier being connected to the shaft of said electric machine, and - said outer ring gear being axially movable between a first operating position in which it is connected in rotation with the planet carrier and a second operating position in which it is blocked on the supporting structure of the unit; and - a device for selection of the transmission ratio for displacing selectively the aforesaid outer ring gear between its two operating positions.