High tensile carbon fibers are provided with a high yield process in which, after oxidation of a precursor, the fibers are first precarbonized in an inert atmosphere to to about 600.degree. C. while imparting 5-10% stretch. In precarbonizing, the fibers are initially heated in a sweeping manner with substantial volumes of hot inert gas which is extracted along with products of decomposition before the fibers are cooled to a low, non-reactive exit temperature. The arrangement minimizes redeposition of tars on the fibers and stretches the fibers in a range in which substantial off-gassing occurs. Thereafter the fibers are finally carbonized at a higher temperature with a different tension being applied, to provide a more reliable less sensitive process that enables oxidation to be effected more rapidly.