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 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 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 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 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 . <EOS>