The process for the production of superfine polymer fibre novwoven fabrics is based on spinning out radically the molten polymer at supply pressure in a rotating nozzle head (6) through a plurality of discharge opening (27) to form fibres and deflecting in the axial direction the not yet completely solidified fibres at a radial distance of 10 mm to 200 mm from the discharge holes (27) by an outer gas stream (8) and afterwards depositing them as nonwoven fabric (15) on a circulating, air-permeable carrier (12). In addition to the outer gas stream (8) an inner gas stream (24) emerges at a lower velocity from a plurality of axial boreholes (23) in the nozzle head (6) at a smaller radial distance than the discharge holes (27). Owing to the centrifugal sweeping forces at the rotating nozzle head (6) a rotationally symmetrical flow field then developes with a predominantly radial velocity component, the temperature of the gas being equal to or greater than the nozzle head temperature.