Filter cigarettes of unit or multiple unit length are produced in a tipping machine wherein successive groups of coaxial plain cigarettes and filter rod sections are caused to roll within a channel bounded by surfaces at least one of which moves relative to the other(s). This results in the conversion of uniting bands, which are carried by successive groups into the inlet of the channel, into tubular sleeves connecting the tubular wrapper(s) of the filter rod section(s) to the plain cigarette(s) of the respective group. The wrappers, and normally also the uniting bands, are perforated in the channel subsequent to, or in part simultaneously with, the conversion of uniting bands into the respective sleeves. Each filter cigarette can be provided with one or more arrays, such as annuli, of perforations, e.g., by mutually inclined laser beams. Rolling movements of successive groups can be accelerated in several stages during and subsequent to entry into the channel, and this also applies for the deceleration of rolling movement ahead of, at and downstream of the outlet of the channel.