the device according to the invention shown in fig2 a has a baffle plate to generate a laminar stream of cooling gas this baffle plate deflects the vertical cooling gas stream into an essentially horizontal gas stream without any abrupt transition that part of fig2 a which is provided to maintain laminar gas flow is shown enlarged in fig2 b the angles drawn into fig2 b preferably have the following values an abrupt transition between the inlet 8 and the baffle plate 9 leads to compression of the air stream with formation of a high degree of turbulence such a device which is not in accordance with the invention is shown in fig3 the device for blowing the gas shown in fig2 b can either form a constructional entity with the spinneret 1 39 or it can be a separate structural unit on which the annular spinneret 1 39 rests insulation not shown is preferably provided between the blowing device and the spinneret to prevent heat transfer from the spinning material to the cooling air it is also desirable that the circular exit slit after deflection of the gas stream opens out to a total opening angle of u2266 22 u00b0 flow resistance to the cooling gas is minimised by the continuous increase in diameter the small total opening angle prevents break up of the stream of cooling gas and allows a turbulent free gas stream to be blown through the filaments it has also been shown that after passage of the gas stream through the fibre bundle part of it returns newly warmed to.