Process for cleaning a regeneration offgas which is obtained in the regeneration of a sorbent laden with a target component by passing a purge gas over or through it, comprising the following process steps: (a) providing the sorbent laden with the target component and the purge gas, (b) introducing the purge gas as continuous purge gas stream into a sorbent vessel containing the laden sorbent and discharging the purge gas stream laden with the target component as regeneration offgas stream from the sorbent vessel, wherein the target component is eluted at some juncture as a peak from the sorbent vessel and an at least partly regenerated sorbent is obtained, (c) introducing the regeneration offgas stream into a gas scrubbing apparatus, contacting the regeneration offgas stream with a scrubbing medium in the gas scrubbing apparatus, discharging the regeneration offgas stream that has been at least partly freed of the target component and the scrubbing medium laden with the target component from the gas scrubbing apparatus, characterized in that, during the entry of the peak of the target component into the gas scrubbing apparatus and for defined periods of time tv, tn before and after the entry of the peak of the target component into the gas scrubbing apparatus, the regeneration offgas stream is contacted with a first volume flow rate of the scrubbing medium and the scrubbing medium laden with the target component is stored at a first pressure in a first intermediate vessel, and in that, for periods before tv and after tn, the regeneration offgas stream is contacted with a second volume flow rate of the scrubbing medium and the scrubbing medium laden with the target component is stored at a second pressure in a second intermediate vessel, wherein: - the first volume flow rate is greater than the second volume flow rate, - for periods before tv and after tn, the scrubbing medium laden with the target component is discharged from the first intermediate vessel and introduced into the second intermediate vessel, wherein the first intermediate vessel is at least partly emptied and wherein the introduction into the second intermediate vessel is effected in such a way that a scrubbing medium stream can be discharged therefrom with a concentration of the target component that varies less over time compared to the regeneration offgas stream and is preferably constant with time, - the scrubbing medium laden with the target component is continuously discharged from the second intermediate vessel and introduced into a scrubbing medium regeneration apparatus, wherein a scrubbing medium at least partly freed of the target component is discharged from the scrubbing medium regeneration apparatus and recycled to the gas scrubbing apparatus, and wherein a stream of matter comprising the target component is also discharged from the scrubbing medium regeneration apparatus. (a) providing the sorbent laden with the target component and the purge gas, (b) introducing the purge gas as continuous purge gas stream into a sorbent vessel containing the laden sorbent and discharging the purge gas stream laden with the target component as regeneration offgas stream from the sorbent vessel, wherein the target component is eluted at some juncture as a peak from the sorbent vessel and an at least partly regenerated sorbent is obtained, (c) introducing the regeneration offgas stream into a gas scrubbing apparatus, contacting the regeneration offgas stream with a scrubbing medium in the gas scrubbing apparatus, discharging the regeneration offgas stream that has been at least partly freed of the target component and the scrubbing medium laden with the target component from the gas scrubbing apparatus, characterized in that, during the entry of the peak of the target component into the gas scrubbing apparatus and for defined periods of time tv, tn before and after the entry of the peak of the target component into the gas scrubbing apparatus, the regeneration offgas stream is contacted with a first volume flow rate of the scrubbing medium and the scrubbing medium laden with the target component is stored at a first pressure in a first intermediate vessel, and in that, for periods before tv and after tn, the regeneration offgas stream is contacted with a second volume flow rate of the scrubbing medium and the scrubbing medium laden with the target component is stored at a second pressure in a second intermediate vessel, - the first volume flow rate is greater than the second volume flow rate, - for periods before tv and after tn, the scrubbing medium laden with the target component is discharged from the first intermediate vessel and introduced into the second intermediate vessel, wherein the first intermediate vessel is at least partly emptied and wherein the introduction into the second intermediate vessel is effected in such a way that a scrubbing medium stream can be discharged therefrom with a concentration of the target component that varies less over time compared to the regeneration offgas stream and is preferably constant with time, - the scrubbing medium laden with the target component is continuously discharged from the second intermediate vessel and introduced into a scrubbing medium regeneration apparatus, wherein a scrubbing medium at least partly freed of the target component is discharged from the scrubbing medium regeneration apparatus and recycled to the gas scrubbing apparatus, and wherein a stream of matter comprising the target component is also discharged from the scrubbing medium regeneration apparatus.