Cellulose fibers or mixtures thereof with synthetic fibers, especially with polyester fibers, are advantageously bleached by means of peroxide or agents capable of splitting off peroxide by adding to a peroxide containing silicate-free bleaching bath as stabilizer amino lower alkylene polyphosphonates and/or hydroxy alkane phosphonates together with hydroxy compounds or polyhydroxy compounds having 2 to 6 carbon atoms in their carbon chain and, if required, with polyamino carboxylic acids. The process according to the present invention has the advantage that deposit formation on the bleaching equipment as well as on the bleached goods is considerably reduced. The decrease in the average degree of polymerization which always takes place on bleaching is less when using the bleaching bath according to the present invention than when using silicate-containing bleaching baths and the degree of whiteness is at least as high as that achieved with silicate-containing bleaching baths while the ash values are considerably reduced, in contrast to those obtained with said silicate-containing baths. When using the combination of phosphonic acid with hydroxy compounds or polyhydroxy compounds, the amount of phosphonic acid can be considerably reduced.
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