Rayon/nylon and other sheath/core composite fibers or other materials, with good adhesion between sheath and core resulting from an adhesion promoter. The adhesion promoter is difunctional and sterically hindered. Fumaric acid and terephthalic acid are preferred adhesion promoters for the composite fibers or other materials, because each compound has both difunctionality and steric hinderance, allowing either to form covalent bonds to both the sheath and the core. Fibers produced in accordance with this invention may be used to produce fabrics which have the strength and wrinkle resistance shown by a number of synthetic fibers, but with the water absorption characteristics of natural fibers such as cotton.