The present invention relates to a polymer composition for peroxide bleaching of a cellulosic fiber material, said composition being in the form of a stable aqueous polymer solution obtained by bringing in an aqueous medium a first polymer (A) comprising a partly or totally acidic homopolymer of acrylic acid, methacrylic acid or maleic acid, or a copolymer of acrylic acid and/or methacrylic acid with an unsaturated dicarboxylic acid, into contact with a second polymer (B) comprising a polylactone of a poly-alfa-hydroxyacrylic acid in solid form or as a moist powder or as a slurry, said polymer solution having a pH of at most 8, The invention also relates to peroxide bleaching processes.