Successive filter cigarettes of unit length or multiple unit length are transported sidways on a first drum-shaped conveyor which cooperates in a filter tipping machine with a second drum-shaped conveyor to rotate successive cigarettes about their respective axes so that the rotating cigarettes come to a temporary halt in a predetermined portion of their path. Such cigarettes are acted upon the two or more laser beams or light beams which are equidistant from and angularly offset relative to each other in the circumferential direction of the cigarette which rotates about its axis so that a circumferentially complete portion of the rotating cigarette is acted upon by radiation while the cigarette completes a fraction of one revolution, namely an angle of 360 degrees divided by the number of beams. The first conveyor has peripheral advancing surfaces for individual cigarettes, and the length of each advancing surface in the circumferential direction of the first conveyor equals the circumferential length of a cigarette divided by the number of beams. The mutual spacing of cigarettes on the first conveyor is less than the mutual spacing of cigarettes on a conveyor which feeds successive untreated cigarettes to the first conveyor ahead of the rolling station and on a conveyor which receives successive treated cigarettes from the first conveyor downstream of the rolling station.