Method for regenerating a nitrogen oxides trap mounted in the exhaust circuit of a motor vehicle internal combustion engine, said exhaust circuit further comprising a catalytic converter for the selective catalytic reduction of the nitrogen oxides downstream of said trap, said method comprising: - a calculation step of calculating a value of the mass of nitrogen oxides (MNOx) stored in the trap; - a comparison step of comparing said mass value (MNOx) against a threshold (Ms); and - when said mass (MNOx) is greater than or equal to said threshold (Ms), a regeneration step (800, 900) of regenerating the trap, in which step the nitrogen oxides are eliminated from the trap by supplying fuel from the engine upstream of the trap, it being possible for said regeneration to be performed in at least a first mode of operation of the engine with a rich mixture, in which mode the nitrogen oxides are reduced, CHARACTERIZED IN THAT it further comprises, when said mass of nitrogen oxides (MNOx) is above said threshold (Ms): - a step of checking whether the conditions for performing said regeneration in said first regeneration mode are met; - a step (600, 700) of checking whether the catalytic converter for the selective catalytic reduction of the nitrogen oxides has at least a predetermined minimum reduction efficiency; - when the first mode is possible and at the same time the catalytic converter efficiency is insufficient, a step of regenerating the trap in said first mode; - when the efficiency of the catalytic converter is sufficient, a step of regenerating the trap by desorption of the nitrogen oxides in a second mode of operation of the engine with a lean mixture, said second mode involving a substantial and rapid increase in the temperature of the trap and a supply of fuel from the engine upstream of the trap. - a calculation step of calculating a value of the mass of nitrogen oxides (MNOx) stored in the trap; - a comparison step of comparing said mass value (MNOx) against a threshold (Ms); and - when said mass (MNOx) is greater than or equal to said threshold (Ms), a regeneration step (800, 900) of regenerating the trap, in which step the nitrogen oxides are eliminated from the trap by supplying fuel from the engine upstream of the trap, it being possible for said regeneration to be performed in at least a first mode of operation of the engine with a rich mixture, in which mode the nitrogen oxides are reduced, - a step of checking whether the conditions for performing said regeneration in said first regeneration mode are met; - a step (600, 700) of checking whether the catalytic converter for the selective catalytic reduction of the nitrogen oxides has at least a predetermined minimum reduction efficiency; - when the first mode is possible and at the same time the catalytic converter efficiency is insufficient, a step of regenerating the trap in said first mode; - when the efficiency of the catalytic converter is sufficient, a step of regenerating the trap by desorption of the nitrogen oxides in a second mode of operation of the engine with a lean mixture, said second mode involving a substantial and rapid increase in the temperature of the trap and a supply of fuel from the engine upstream of the trap.