In a vehicle provided with a power propulsion system of the mild-hybrid type, a BAS unit—including an electric machine connected through a belt transmission to the shaft of an internal combustion engine—is exploited as the only propulsion engine of the vehicle in given operating conditions. The internal combustion engine is provided with a system for variable actuation of the intake valves which is controlled to reduce the pumping losses of the internal combustion engine in the phase in which such engine is in cut-off condition and it is driven by the aforementioned BAS unit. It is also provided for that the system for variable actuation of the intake valves be controlled to temporarily increase the pumping losses of the internal combustion engine in a phase in which it is required to accelerate the switching off of the engine.