PURPOSE: To continuously oxidize a continuous web of an organic fiber controlling the temperature of fiber web while maximizing passing speed of the web through an oxidizing chamber and to efficiently utilize heat supplied from the oxidizing chamber.

CONSTITUTION: In this method and apparatus for continuously oxidizing an organic fiber web, many webs 2 are passed in parallel through a oxidizing chamber 1 and enter and leave the chamber through appropriate slots, and after leaving the chamber passes around a cooling cylinder 5, 5' and 5" external to the chamber. The cooling cylinder lowers the temperature of the web an appropriate amount prior to the next pass. The alternate passes are as close as conveniently possible to each other. The interior surfaces of the chamber are so highly reflective that enables the most efficient use of heat required by the system. The passing speed of the web through the chamber is maximized.