Abstract: Apparatus for making perforations in continuous or interrupted webs of cigarette paper or the like has one or more perforating units serving to direct radiant or electrical energy against selected portions of the web to make holes therein. That portion of each perforating unit which surrounds the locus of propagation of energy beyond the respective perforating unit is externally cooled and cleaned by one or more streams of compressed gas which ensure that such portion cannot accumulate solid combustion products which could interfere with the propagation of energy toward the web. The stream or streams are furnished by the orifices of nozzles which can be provided in the carrier or carriers for the perforating units or can be outwardly adjacent to the carrier or carriers.