In order to clean the webs in a belt buffer having a plurality of belts arranged one above the other, a cleaning medium is applied to a running belt by means of a cleaning device and vacuumed off together with the loosened contamination. A device for carrying out this cleaning has a cleaning head for applying and vacuuming off the cleaning medium and a device for adjusting the height of the cleaning head to the level of the web to be cleaned and to move the cleaning head over the web to be cleaned.