Abstract: The invention suggests a procedure for the desulfurization of a storage catalyst, whereby the storage catalyst is run with a desulfurization temperature range that is required for the desulfurization, and whereby the storage catalyst is admitted with a regeneration gas with an air lambda of max. 1, as well as a device for the implementation of the procedure. During the desulfurization the storage catalyst is admitted in temporal shifts with a regeneration gas with an air lambda of max. even 1 during a desulfurization phase and a regeneration gas with an air lambda of higher than 1 during a desulfurization pause. Upstream before the storage catalyst an incoming lambda signal and downstream after the storage catalyst an outgoing lambda signal is acquired. By comparing the two signals that have been acquired during a desulfurization phase at least one favorable point of time for terminating the desulfurization process can be noticed.