An oxidation furnace for the oxidative treatment of fibers, in particular for producing carbon fibers, including a housing, which is gas-tight, apart from passage areas for the fibers, and a process chamber located in the interior of the housing. By an atmosphere device, a hot working atmosphere can be produced and blown into the process chamber. Deflecting rollers, which are arranged outside of the process chamber in deflecting areas, guide the fibers through the process chamber in a serpentine manner so that the fibers lie next to one another as a fiber carpet, wherein the fiber carpet spans a plane between opposite deflecting rollers. Outlet fiber carpets of outlet fibers that have left the process chamber and are on the way to a deflecting roller can be cooled in a specific manner by a fiber-cooling device before the outlet fiber carpets reach the deflecting roller.