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 that is solid at room temperature and at atmospheric pressure (ii)； at least one fatty ester, which is solid at room temperature and at atmospheric pressure (iii)； at least one surfactant (iv)； at least one basifying agent (v) and/or at least one dye (vi) chosen from oxidation dyes and direct dyes, and mixtures thereof； composition (B) comprising, in a cosmetically acceptable medium, at least one oxidizing agent. The invention also relates to a non-oxidizing composition (A) in the form of a direct emulsion. Lastly, the invention relates to a multi-compartment device.
