Abstract: The invention relates to a stabilizing composition comprising following components (A) a polymer having the following formula: wherein R1 is a hydrogen atom or an alkyl group containing 1 to 12 carbon atoms, R2 is —COOM or —CH2COOM, M is a hydrogen atom, an alkali metal ion, an alkaline earth metal ion, an ammonium ion or a mixture thereof, n, m and k are molar ratios of corresponding monomers, wherein n is 0 to 0.95, m is 0.05 to 0.9, and k is 0 to 0.8, and (n+m+k) equals 1, and the weight average molecular weight is between 500 and 20,000,000 g/mol, (B) a chelating agent, (C) a poly-alpha-hydroxyacrylic acid or an alkaline salt thereof or the corresponding polylactone thereof, and (D) optionally a polycarboxylic acid polymer or an alkaline salt thereof. The invention also relates to a process for the treatment of a fiber material.