In this paper we report on the influence of substituents on the degradation of azo reactive dyes based on H-acid caused by the action of hydrogen peroxide in aqueous solution and on cellulose. The results support the view that the perhydroxyl radical anion is the active agent in the dye degradation by hydrogen peroxide. We suggest that, predominantly, the dissociated form of the ortho-hydroxyazo dyes undergoes the degradation, and thus the pK(a) value of the dye is an important criterion for the fastness to peroxide. With this background, an expanded version of the Hammett correlation including the pK(a) values of the dyes yields a linear free energy relationship. On cellulose, bifunctional reactive dyes seem to be more stable to peroxide bleaching liquor than monofunctional reactive dyes with comparable pK(a) values.