The single-walled and double-walled collective chimney system is intended for assembly in multi household buildings, in multi-storey buildings. It allows to flue gas discharge at the same time from several condensing boilers placed on many floors. The system, apart from flue gas discharge, enables to supply of combustion air by the space created by the hermetic housing of chimney (chimney shaft) or by the space created by the outer sheath tube of chimney