Lightening or coloring of keratin fibers, particularly human keratin fibers such as hair, comprises applying an anhydrous cosmetic composition (A) comprising one or more fatty substances and one or more surfactants, a cosmetic composition (B1) comprising one or more ammonium salts, and a composition (C) comprising one or more oxidizing agents, to the keratin fibers, when the process is for dyeing keratin fibers, the composition (B1) further comprises one or more oxidation dyes and/or direct dyes. An independent claim is included for a multi-compartment device comprising first compartment containing the composition (A), a second compartment containing the composition (B1) with one or more ammonium salts and optionally one or more oxidation dyes, one or more direct dyes or their mixtures, and a third compartment containing the composition (C).
