A method of operating an aftertreatment system of an internal combustion engine having a lean nitrogen-oxides trap and a reductant storage device placed downstream of the lean nitrogen-oxides trap is disclosed. A regeneration of the lean nitrogen-oxides trap is performed. During the regeneration, a reductant concentration between the lean nitrogen-oxides trap and the reductant storage device is measured. An amount of reductant produced by the nitrogen-oxides trap is calculated on the basis of the measured concentration. The amount of reductant produced may be used to stop regeneration of the LNT if this amount reaches the maximum available storage capacity, or to trigger a test of the proper functioning of the reductant storage device if there is at least a minimum amount of reductant available, or to switch to another operation mode of the reductant storage device and/or the LNT, in particular if this amount is larger than a threshold value.