Blocks of plain or filter cigarettes are accumulated in at least two group building assemblies each of which comprises at least two block forming units receiving cigarettes by gravity flow by way of upright ducts. The assemblies are adjacent the path of a series of successive receptacles which serve to transport discrete blocks stepwise to a multiple-track packing machine. The units accumulate blocks of cigarettes during intervals which include the duration of at least one stepwise movement of the receptacles and that of at least one period of standstill of the receptacles. Such intervals suffice to ensure satisfactory gathering of cigarettes into blocks of required size and shape at a frequency which is required for full-speed operation of the multiple-track packing machine.