Abstract: In the course of producing acrylic fibers, the spun filament bundle before the heat stretching treatment is subjected to a special stretching treatment in a warm water bath under a specific condition so that the degree of filament separability of said spun filament bundle traveling through the heat stretching step will be maintained within a prescribed range, and when the acrylic fibers so prepared are heat-treated for carbonization, carbon fibers representing a peculiar load-elongation behavior can be produced in an industrially advantageous manner.

Abstract: Carbon fibers having excellent physical properties and satisfactory quality uniformity are produced in an industrially advantageous manner by heat-treating acrylonitrile filaments so prepared that a specified amount of the sulfonic acid groups (--SO.sub.3 H) which have been introduced into the fiber is converted to its salt form (--SO.sub.3 X) and that the degree of filament separability of the spun fiber-bundle traveling through the heat stretching step is maintained within a specified range.