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 a 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 at a distance from by 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: - the shaft of the electric machine is connected to the crank shaft of the internal-combustion engine at the end thereof opposite to the end connected to the gearbox device by means of a belt transmission including an endless belt engaged on a first pulley connected to the shaft of the electric machine and on a second pulley connected to the shaft of the internal-combustion engine; - said unit further comprises one or more auxiliary devices of the motor vehicle, such as, for example, a compressor for an air-conditioning system and a source of negative pressure for the braking system; - said belt transmission controls said one or more auxiliary devices via an auxiliary shaft arranged coaxially with respect to the shaft of the electric machine; and - said one or more auxiliary devices are mounted coaxially with respect to the shaft of the electric machine. - an internal-combustion engine; and - a gearbox device including: - at least one primary shaft, that can be connected to a 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 at a distance from by 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, - the shaft of the electric machine is connected to the crank shaft of the internal-combustion engine at the end thereof opposite to the end connected to the gearbox device by means of a belt transmission including an endless belt engaged on a first pulley connected to the shaft of the electric machine and on a second pulley connected to the shaft of the internal-combustion engine; - said unit further comprises one or more auxiliary devices of the motor vehicle, such as, for example, a compressor for an air-conditioning system and a source of negative pressure for the braking system; - said belt transmission controls said one or more auxiliary devices via an auxiliary shaft arranged coaxially with respect to the shaft of the electric machine; and - said one or more auxiliary devices are mounted coaxially with respect to the shaft of the electric machine.