Abstract: A flameresisting apparatus in which two sections, referred to as roller compartments, enclosing a series of rollers provided face to face with one another for transferring precursor fiber, are separated from a heat treatment section by two walls facing each other. The walls include apertures for passage of the precursor fiber. Significantly, the two walls facing each other are provided at a distance which enables the precursor fiber to pass from one wall to the other in 5 to 60 seconds. The surface temperature of the rollers and the temperature of the roller compartments are maintained at a temperature of 10.degree. to 80.degree. C. lower than the temperature of the heat treatment compartment, but not lower than 180.degree. C. In addition, heated air is blown against the precursor fiber into the heat treatment compartment.