A process for evaluating performance deterioration of a nitrogen oxide storage catalyst which has a nitrogen oxide storage function and an oxygen storage function and is operated with cyclic alternation of the air/fuel ratio in the exhaust gas from lean to rich. The nitrogen oxides are stored during the lean phase and the nitrogen oxides are desorbed and converted during the rich phase. To check the serviceability of the storage catalyst, the air/fuel ratio of the exhaust gas is switched from lean to rich and the rich phase is extended beyond the time required for complete desorption of the nitrogen oxides until at least the rich exhaust gas passes right through the catalyst and the time interval &Dgr;t1 produced between the first change-over until breakthrough of the rich exhaust gas and, after again switching from rich to lean running, the time interval &Dgr;t2 produced between the second change-over and passage of oxygen through the catalyst are measured and the time differences &Dgr;t1 and &Dgr;t2 are used for separate assessment of the oxygen storage function and the nitrogen oxide storage function of the catalyst.