The present invention relates to a composition for dyeing keratin fibers, comprising: at least one nonionic ether of a polyoxyalkylenated fatty alcohol of formula (i) R—(O-Alk)nOR′ (i), in which: —R denotes a linear or branched, saturated or unsaturated C10-C30 hydrocarbon-based radical, —R′ denotes a linear or branched, saturated or unsaturated C10-C30 hydrocarbon-based radical, which may be substituted with a hydroxyl radical, —n is an integer between 1 and 100 inclusive, and —Alk represents a linear or branched, preferably linear, (C1-C6)alkylene group such as ethylene or propylene, preferably ethylene, —at least one fatty alcohol comprising at least 20 carbon atoms; —at least one chemical oxidizing agent. The present invention also relates to a process using this composition, and to a multi-compartment device that is suitable for implementing the invention.
