The coaxial strands of tobacco or filter material are formed using a first machine (20) to produce the first strand from strip-type wrapping material and a strand of filler material. A second machine produces the coaxial strand from the first strand, second strip-type wrapping material, and a strand of filler material. - The strand (12) from the first machine is held in a buffer storage unit before further processing in the second machine. It is pref. deposited in a storage vessel (10), from which it is extracted and fed to the second machine.