Successive cigarettes of a series of cigarettes, such as filter cigarettes, are transported sideways in the axially parallel peripheral flutes of a rotary drum-shaped conveyor to the inlet(s) of a straight or V-shaped rolling channel or of two successive straight channels defined by the rolling surface(s) of one or two stationary block-shaped rolling members and the external surface of an endless belt trained over several rollers and being at least partially confined in a recess or groove of the conveyor in such a way that the surface(s) of the rolling member(s) cooperate with the surface of the belt to roll successive cigarettes in the channel or channels about their longitudinal axes while one or more beams issuing from one or more lasers or other radiation source(s) impinge upon the wrappers of the cigarettes rolling in the channel or channels. The belt lifts successive cigarettes out of the respective flutes at the inlet and permits successive treated cigarettes to enter oncoming empty flutes at the outlet of the single rolling channel or each rolling channel.