In a motor vehicle having exhaust-gas recirculation, the fluid of the air-conditioning circuit is used to cool the coolant of a dedicated hydraulic circuit, which in turn cools the recirculated exhaust gases in a two-stage (HT,LT EGR) heat exchanger, thus increasing engine gain by replenishing in order to reduce NOx emissions. The method comprises differentiated control strategies for these circuits, as a function of vehicle driving conditions, continuous modes and transient braking and acceleration modes, in order to compensate for the consumption of the compressor (C) of the air-conditioning circuit. The circuits comprise a heat exchanger (EXCH STORE) for heat exchange between the air-conditioning fluid and coolant, provided with a bypass, capable of accumulating and releasing cold energy, and, optionally, a line for condensing the water vapour of the exhaust gases and for reinjecting the condensed water to the intake.