Tandem cyclone separator, consisting of an integrated series connection of 2/3 cyclone separators, at least one of which having special constructional measures for producing one or more jets of dust. The measures are annular grooves or screw-shaped webs which both open into window-shaped openings from where a partial gas stream can be fed back via return lines and possible blowers into a sub-cyclone arranged upstream. The stream can be returned via a jet blower or into a suction venturi nozzle. The return line can open into the axis of the cyclone or tangentially obliquely into the precipitation space. Guiding devices for the stream of gas are provided in the cyclone and the gas outlet.