The present invention relates to a process for dyeing or lightening human keratin fibers, which consists in extemporaneously mixing at the time of use two compositions (A) and (B) and in applying the mixture to the fibers the said mixture comprising at least 25% by weight of fatty substances relative to the total weight of the mixture of compositions (A) (B) with: composition (A) being in the form of a direct emulsion comprising: at least 30% by weight of oil(s) (i) at least one fatty alcohol having at least 20 carbon atoms in its longest hydrocarbon chain (ii) at least one surfactant (iii) at least one basifying agent (iv) and optionally at least one dye chosen from oxidation dyes and direct dyes, and mixtures thereof (v) composition (B) comprising at least one oxidizing agent. The invention also relates to compositions (A), the mixture of the aforementioned compositions (A) and (B), and a multi-compartment device.
