Abstract: The present invention is drawn to new processes for sequential oxidative and reductive bleaching of fibers (e.g. natural, synthetic, or blends thereof) e.g. in a single bath, which provide superior bleaching with less physical damage. Said processes comprising the steps of: (1) bleaching fibers with hydrogen peroxide; (2) adding either, (a) a material which combines with hydrogen peroxide to form a reductive bleaching agent, or (b) an inactivating material to inactivate unspent hydrogen perioxide with subsequent addition of a reductive bleaching agent, and; (3) reductively bleaching the already oxidatively bleached fibers. Also encompassed by the present invention are novel bleached fibers produced by the aforementioned processes, having highly advantageous and desirable properties e.g. a high degree of whiteness with low degree of damage.