Abstract: A method of bleaching a cellulosic fiber material with hydrogen peroxide, comprising:(a) impregnating a cellulosic fiber material with an aqueous bleaching solution containing hydrogen peroxide and a stabilizer comprising:(i) 1 to 100 parts by weight of at least one hydroxyacrylic acid polymer selected from the group consisting of poly-.alpha.-hydroxyacrylic acids, and salts thereof and polylactone corresponding thereto; and(ii) 1 to 50 parts by weight of at least one organic phosphate acid compound selected from the group consisting of methylene,1,1-diphosphonic acid, ethylidene-1,1-diphosphonic acid, butylidene-1,1-disphosphonic acid, 1-hydroxyethylidene-1,1-diphosphonic acid, 1-hydroxypropyl-idene-1,1-diphosphonic acid, amino-tri(methylenephosphonic acid), hexamethylene diamine tetra(methylenephosphonic acid), triethylenetetramine hexa(methylenephosphonic acid), and salts of the above-mentioned organic phosphonic acids, and(b) heating the impregnated cellulosic fiber material with steam.