Abstract: The invention relates to a process for the manufacture of carbon and/or graphite fibres from natural organic fibres, obtained particularly from the distillation residues of coal or petroleum, by irradiation by microwaves.The process according to the invention consists in subjecting the fibres to a preparatory thermal treatment up to a temperature of between 300.degree. and 1500.degree. C. in an inert atmosphere, for example of nitrogen, argon, helium or hydrogen and then irradiating them with microwaves.The microwaves may have frequencies between 900 and 30,000 MHz and preferably between 2000 and 15,000 MHz and use a power of between 10W and 30kW and preferably between 50W and 10kW. The irradiation is preferably also in an inert atmosphere, for a period ranging from 10 seconds to 15 minutes. The fibres may be oxidized for example in an atmosphere of oxygen, ozone or air up to a temperature of between 100.degree. and 250.degree. C. before the preparatory thermal treatment.