A process for the production of hollow carbon fibres by the treatment of a stabilised carbon fibre precursor in an application device using high-frequency electromagnetic waves. The application device includes structure supplying the electromagnetic waves to a outcoupling region and a hollow outer conductor terminating in the outcoupling region. For the treatment, a field of the high-frequency electromagnetic waves is generated and a field strength in the range from 15 to 40 kV/m is set in the outcoupling region of the application device. The stabilised carbon fibre precursor is conveyed continuously as an inner conductor through the hollow outer conductor, thereby forming a coaxial conductor having an outer and an inner conductor, and through the subsequent outcoupling region. An inert gas atmosphere is created in the coaxial conductor and in the outcoupling region by passing through an inert gas.