in the second hot zone the fibers are subjected to a heat treatment at about 500 u00b0 700 u00b0 c for a period of about 10 to 60 seconds thereafter they are passed through another curtain of inert gas then to a third hot zone which is usually heated to a temperature having an incline of from about 750 u00b0 to a temperature of 900 u00b0 c or more than 900 u00b0 c but not more than 950 u00b0 c by heating element 4c the fibers are retained in this zone for about 5 to 40 seconds the temperatures provided by heating elements 4a 4b and 4c vary stepwise but the temperature within the heating tube gradually increases from top to bottom finally the fibers are recovered from the system through fiber outlet 7 and a sealing mechanism a preferred sealing mechanism is the combination of a curtain of nitrogen gas and a roller seal the recovered fibers that have been carbonized to a small extent so called pre carbonized are then fed to a furnace which is held at a higher temperature of about 900 u00b0 to 1 500 u00b0 c in an inert gas atmosphere and by holding them in that furnace for a period of about 35 to 200 seconds carbon fibers having the following properties are obtained ______________________________________fineness 790 810 textensile modulus of elasticity 23 900 25 000 kg mm sup 2ultimate tensile strength 415 450 kg mm sup 2 co efficient of variation cv 4 or lesselongation at failure 1 72 1 86 ______________________________________ the apparatus of the present invention can be operated continuously for example for 480 hours with 300 bundles.