A method for the desulfurization of a nitrogen oxide adsorber of an exhaust gas purification device for a combustion system employs desulfurization phases that are intermittently implemented by a desulfurization control unit. During each desulfurization phase, the carbon monoxide concentration and/or the lambda value of the exhaust gas stream exiting the nitrogen oxide adsorber is recorded. A localized maximum that appears in the recorded course of the carbon monoxide concentration over time, or a downward slope that appears in the established course of the lambda value over time, falling from a temporary plateau value, is employed as criterion for terminating the desulfurization phase. The method may be used, for example, in exhaust gas purification devices in primarily lean-burning vehicle combustion engines.