Abstract: A process for continuous production of carbon fibres whereby stabilised precursor fibres are carbonised and graphitised with the help of high-frequency electromagnetic waves, characterised in that the stabilised precursor fibres are continuously conveyed, as the inner conductor of a coaxial conductor consisting of an outer and an inner conductor, through the coaxial conductor and a treatment zone; that the stabilised precursor fibres are irradiated in the treatment zone with high-frequency electromagnetic waves that are absorbed by the precursor fibres, which are thereby heated and converted into carbon fibres; and that the stabilised precursor fibres or carbon fibres are conveyed under an inert gas atmosphere through the coaxial conductor and the treatment zone.