A stabilizing agent for peroxide-bleaching procedure includes (A) a component including a homopolymer or copolymer of α-hydroxyacrylic acid or water soluble salt or polylactone of the homo- or co-polymer, (B) a component including a homopolymer or copolymer of acrylic acid, methacrylic acid and/or maleic acid and water-soluble salt of the homo- or co-polymer, (C) a component including DTPA, TTHA or water-soluble salt thereof and optionally (D) a component including a water-soluble inorganic Mg salt and is used to pretreat a fiber material with a pretreating liquid containing the stabilizing agent before bleaching with peroxide, or to bleach the fiber material by a bleaching liquid containing a peroxide bleaching agent and the stabilizing agent.