The present invention relates to the use of a particular, generically defined copolymer for stabilization of a peroxidic compound against breakdown. The present invention further relates to a particular embodiment of the copolymer, namely a copolymer comprising repeat units derived from N-vinylpyrrolidone (or from N-vinyl-2-caprolactam) and at least one comonomer which is selected from the group consisting of vinylphosphonic acid, 2-acrylamido-2-methylpropanesulfonic acid and combinations of these monomers.