Abstract: Cosmetic composition for the oxidative treatment of hair or skin, prepared by mixing of at least two components, in which dehydroascorbic acid or a dehydroascorbic acid salt or a dehydroascorbic acid derivative is generated from ascorbic acid, ascorbic acid derivative and ascorbic acid salt prior to application by an enzyme that catalyzes the enzymatical oxidation of said of ascorbic acid as well as a process for carrying out the oxidative treatment of keratin, particularly for the oxidative post-treatment of reduced hair in the process of permanent deformation of hair using said composition.