The invention relates to a method of and to an apparatus for perforating the tubular wrappers of plain or filter cigarettes and other rod-shaped articles of the tobacco processing industry. The articles are advanced sideways at the periphery of a rotary drum-shaped carrier which cooperates with a device serving to roll them about their longitudinal axes while the wrappers are being perforated by one or more pulsating beams issuing from one or more lasers and passing through a stationary cylinder lens on their way to the facets of a rotating cylindrical mirror which directs the beam(s) across the axis of the carrier and pivots the beam(s) about such axis on its or their way radially outwardly of the carrier toward a first set of stationary deflecting mirrors. These mirrors deflect the beam(s) in at least substantial parallelism with the axis of the carrier at locations radially outwardly of the latter's periphery toward a second set of deflecting mirrors which, in turn, direct the beam(s) substantially radially toward the axis of the carrier and against spherical lenses which focus the beam(s) upon the wrappers of the articles.