The desulfation of a NOx storage catalytic converter takes place in two phases. In a first phase, the NOx storage catalytic converter is alternately exposed to rich and lean exhaust gas. In a subsequent second phase, the NOx storage catalytic converter is operated using rich exhaust gas. This method permits the quantity of hydrogen sulfide that occurs during the desulfation process to be minimized and achieves at the same time an efficient removal of sulfate from the deep-seated layers of the NOx storage catalytic converter.