The present disclosure relates to a process for lightening or dyeing keratin fibers, for example, human keratin fibers such as the hair, comprising applying to the keratin fibers: (a) an anhydrous cosmetic composition (A) comprising at least one fatty substance and at least one surfactant; (b) a cosmetic composition (B) comprising at least one ammonium salt; and (c) a composition (C) comprising at least one oxidizing agent; when the process is a process for dyeing keratin fibers, said cosmetic composition (B) further comprises at least one oxidation dye and/or at least one direct dye. The present disclosure also relates to a multi-compartment device comprising the disclosed compositions for lightening or dyeing keratin fibers.