Provided is a process for lightening or dyeing keratin fibers, including human keratin fibers such as the hair, in the presence of an oxidizing agent, wherein the following are applied 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 organic amine with a pKb of less than 12 at 25° C. and at least one mineral base, and (c) a composition (C) comprising at least one oxidizing agent; when the process described herein is a process for dyeing keratin fibers, composition (B) further comprises at least one dye. Also provided is a multi-compartment device comprising a first compartment having the anhydrous cosmetic composition, a second compartment having at least one organic amine with a pKb of less than 12 at 25° C., and also at least one mineral base and optionally at least one dye, and a third compartment having an oxidizing composition.