The present disclosure relates to a composition for dyeing or lightening human keratin fibers, comprising: a cosmetically acceptable medium; at least 25% by weight of at least one fatty substance different from fatty acids; from 1% to 10% by weight of at least one nonionic surfactant comprising ethylene oxide in an amount ranging from 10 mol to 80 mol; at least one dye chosen from oxidation dyes and direct dyes; at least one basifying agent; and at least one oxidizing agent. The disclosure also relates to a dyeing or lightening process using it. Another subject of the disclosure is multi-compartment devices or kits for obtaining, after mixing together the compositions of the compartments, just before its application, a composition according to the disclosure.