In a mode of driving of a hybrid automotive vehicle in which only the electric machine (MEL) is used to propel the vehicle: when the accelerator pedal is in a position corresponding to a demanded torque value that is higher than or equal to the maximum torque (CMELMAX) that the electric machine can supply and strictly below a set threshold (S), the combustion engine remains switched off and the electric machine supplies this maximum torque (CMELMAX); and when the accelerator pedal is in a position corresponding to a demanded torque value greater than or equal to the threshold (S), the combustion engine is started automatically and supplies a torque such that the value of the total torque supplied by the electric machine and the combustion engine is equal to the demanded torque value.