The system (CVT) includes a first electrical machine (M1) with a first rotor (R1) provided with a multiphase winding (W1) and fixed firmly to the shaft (1) of the internal combustion engine (ICE) and a second rotor (R2) or intermediate rotor coaxial with the first rotor (R1) and carrying first magnetic means (PM1) operatively cooperating with the winding (W1) of the first rotor (R1), the intermediate rotor (R2) being coupled with at least one axle (2) of the motor vehicle, and a second rotary electrical machine (M2) coaxial with the first (M1) and including a stator (ST), which is arranged on the opposite side of the intermediate rotor (R2) to the first rotor (R1) and is provided with a multiphase winding (W2), as well as the intermediate rotor (R2) which also carries second magnetic means operatively cooperating with the winding (W2) of the stator (ST), a first inverter and a second inverter (I1, I2) of which the a.c. sides are connected to the winding (W1) of the rotor (R1) and to the winding (W2) of the stator (ST), respectively, and the respective d.c. sides are connected in parallel with one another by means of a d.c. voltage link (L), sensors (S1-Sn) suitable for providing electrical signals indicative of predetermined parameters relating to predefined operating conditions of the internal combustion engine (ICE) and of the motor vehicle, and an electronic control unit (ECU) connected to the sensors (S1-Sn) and to the inverters (I1, I2) and arranged to control the operation of the inverters (I2, I2) in a manner such that, after the engine (ICE) has been started, the voltage (VDC) in the d.c. voltage link (L) is regulated to a predetermined value which is variable in accordance with predetermined procedures in dependence on the values of the parameters monitored by the sensors (S1-Sn).