Separation functional fibers are produced by exposing fibers with a core/sheath structure to an ionizing radiation and then grafting a polymerizable monomer to the fibers. Ion-exchange fibers are produced by introducing, through radiation-initiated graft polymerization, ion-exchange groups into the sheath of each of composite fibers the core and the sheath of which are composed of different kinds of high-polymer components. The separation functional fibers and the ion-exchange fibers are useful in various applications such as the production of pure water in electric power, nuclear, electronic and pharmaceutical industries and the demineralization of high-salt content solutions in the production of foods and chemicals. The fibers are also useful in removing harmful components from gases, as well as odorous components such as ammonia.