A cyclonic separation apparatus comprises a plurality of series-connected separation stages 50,51, each comprising a plurality of cyclone separators 16/23 connected in parallel and disposed in a generally annular arrangement about a main vertical axis of the apparatus, with their respective longitudinal cyclone axes extending parallel to the main axis. The successive separation stages 50,51 in the direction of fluid flow are disposed radially inwardly of each other with respect to the main axis of the apparatus and are also vertically staggered upwardly, so that the outlet 20 of one separation stage 50 leads directly into the inlet 22 of the next downstream stage 51. The multi-stage, series connected cyclone separators of the apparatus provide a high separation efficiency, yet the annular arrangement of the stages 50,51 makes the apparatus compact and enables the apparatus to be utilized in a vacuum cleaner.