The invention relates to a method for dyeing or lightening human keratinous fibres in which: (a) an anhydrous composition (A) comprising one or more fatty substances and one or more surfactants; (b) a composition (B) comprising one or more oxidizing agents and optionally one or more fatty substances; (c) a composition (C) comprising one or more alkaline agents and optionally one or more oxidation dyes and/or one or more direct dyes, are applied to the said fibres, the said fatty substance or substances being chosen from volatile linear alkanes, additional fatty substances and their mixtures, and it being understood that one or more volatile linear alkanes is or are present in at least one of the compositions (A), (B) or (C) and preferably in at least one of the compositions (A) and (B). The invention also relates to a device comprising the three compositions (A), (B) and (C) in three different compartments and to a ready-for-use composition resulting from the mixing of the compositions (A), (B) and (C).