In a known process for the manufacture of a preform for optical fibres of quartz glass using a plasma burner, this is operated in a deposition phase and a smoothing phase, a silicon-containing starting substance being supplied to the plasma burner during the deposition phase, SiO 2 being formed therefrom in a plasma flame allocated to the plasma burner and this SiO 2 being deposited in layers on the cylinder jacket surface of a substrate body rotating around its own longitudinal axis by reversing movement of the plasma burner along the substrate body and being vitrified directly during this process into quartz glass of the preform and the preform surface being treated during the smoothing phase, by the plasma flame moving at least once along the preform, with a temperature which is higher in comparison with deposition phase such that smoothing of the preform surface and melting of the near-surface bubbles are effected. In order to indicate an economic process on this basis which allows the manufacture of low bubble content or bubble-free preforms with an acceptable time and material expenditure, it is suggested according to the invention that the deposition phase comprises a multiplicity of successive deposition sub-phases in the course of which a quartz glass layer is produced in a thickness of less than 400 µm, successive deposition sub-phases being interrupted by a smoothing phase.