Method for purging a nitrogen oxides trap mounted in the exhaust circuit of an internal combustion engine, in a motor vehicle drive device, said method comprising: - a step during which a current mass of nitrogen oxides (M NOX) in the trap is determined, while the engine is running with a lean mixture; - a step during which a need to purge the trap is detected, when said mass reaches a threshold value; - a step of transiently regulating the engine towards a steady-state setting with a steady-state rich mixture, during which step the quantity of air is decreased and the quantity of fuel admitted into the engine is increased by commanding movements of actuators in the engine air and fuel injector lines; - a step of actually purging the trap, during which step said engine rich-mixture steady-state setting is applied, for as long as a set of engine and vehicle operating conditions (N,C,V,dC/dt,dV/dt) that allow the purge to take place remain satisfied; and - a step of interrupting the purge when the said conditions are no longer satisfied, CHARACTERIZED IN THAT it further comprises, in the event that the purged duration (t part), equal to the sum of the duration of the said step of transient regulation (t trans) of the engine and of the duration of the actual purging step (t purge) up to the point at which it is interrupted, is below a predetermined first partial-purge duration threshold value (t seuil1): - a step in which the engine adopts a specific lean-mixture pending setting, in which the quantity of fuel admitted to the engine is decreased but the position of the actuators in the engine air line is not modified in comparison with the rich-mixture steady-state setting; and - a step of returning the engine setting to its rich-mixture steady-state setting when the engine and vehicle operating conditions (N,C,V,dC/dt,dV/dt) that allow the purge to take place are regained. - a step during which a current mass of nitrogen oxides (M NOX) in the trap is determined, while the engine is running with a lean mixture; - a step during which a need to purge the trap is detected, when said mass reaches a threshold value; - a step of transiently regulating the engine towards a steady-state setting with a steady-state rich mixture, during which step the quantity of air is decreased and the quantity of fuel admitted into the engine is increased by commanding movements of actuators in the engine air and fuel injector lines; - a step of actually purging the trap, during which step said engine rich-mixture steady-state setting is applied, for as long as a set of engine and vehicle operating conditions (N,C,V,dC/dt,dV/dt) that allow the purge to take place remain satisfied; and - a step of interrupting the purge when the said conditions are no longer satisfied, CHARACTERIZED IN THAT - a step in which the engine adopts a specific lean-mixture pending setting, in which the quantity of fuel admitted to the engine is decreased but the position of the actuators in the engine air line is not modified in comparison with the rich-mixture steady-state setting; and - a step of returning the engine setting to its rich-mixture steady-state setting when the engine and vehicle operating conditions (N,C,V,dC/dt,dV/dt) that allow the purge to take place are regained.