A method for cleaning exhaust gas by operating an internal combustion system, the internal combustion system comprising: an exhaust gas cleaning device for cleaning exhaust gas by redox, comprising an exhaust gas cleaning catalyst having at least one type of metal of noble metals and transition metals, NOx-absorbing material for absorbing and releasing nitrogen oxides according to the surrounding nitrogen oxide concentration, and a compound represented by A 2 O 2 SO 4 and/or A 2 O 2 S, with A being a rare earth element, and a control component for switching the operating mode of the internal combustion engine between a first mode in which the air/fuel ratio of the combustion in the internal combustion engine is controlled to the stoichiometric ratio, and a second mode in which the air/fuel ratio of the combustion in the internal combustion engine results in an excess of oxygen, wherein the method comprises: introducing the exhaust gas discharged from an internal combustion engine into the exhaust gas cleaning device, selecting the first mode when the engine load is greater and selecting the second mode when the engine load is lower, wherein the second mode includes a rich spike, which temporarily suspends lean operations in which the air/fuel ratio results in an excess of oxygen, to perform a fuel-rich operation in which the exhaust gas is a reducing atmosphere that is rich with reducing agents such as HC or CO. an exhaust gas cleaning device for cleaning exhaust gas by redox, comprising an exhaust gas cleaning catalyst having at least one type of metal of noble metals and transition metals, NOx-absorbing material for absorbing and releasing nitrogen oxides according to the surrounding nitrogen oxide concentration, and a compound represented by A 2 O 2 SO 4 and/or A 2 O 2 S, with A being a rare earth element, and a control component for switching the operating mode of the internal combustion engine between a first mode in which the air/fuel ratio of the combustion in the internal combustion engine is controlled to the stoichiometric ratio, and a second mode in which the air/fuel ratio of the combustion in the internal combustion engine results in an excess of oxygen, wherein the method comprises: introducing the exhaust gas discharged from an internal combustion engine into the exhaust gas cleaning device, selecting the first mode when the engine load is greater and selecting the second mode when the engine load is lower, wherein the second mode includes a rich spike, which temporarily suspends lean operations in which the air/fuel ratio results in an excess of oxygen, to perform a fuel-rich operation in which the exhaust gas is a reducing atmosphere that is rich with reducing agents such as HC or CO. introducing the exhaust gas discharged from an internal combustion engine into the exhaust gas cleaning device, selecting the first mode when the engine load is greater and selecting the second mode when the engine load is lower, wherein the second mode includes a rich spike, which temporarily suspends lean operations in which the air/fuel ratio results in an excess of oxygen, to perform a fuel-rich operation in which the exhaust gas is a reducing atmosphere that is rich with reducing agents such as HC or CO.