The present invention relates to a process for lightening or dyeing keratin materials, in which the following are used: a) a direct emulsion (A) comprising one or more fatty substances in an amount of greater than 25% by weight one or more oxyalkylenated nonionic surfactants an amount of water of greater than 5% by weight relative to the total weight of the emulsion, and one or more oxidizing agents, and b) a composition comprising one or more alkaline agents. The invention also relates to a multi-compartment device comprising, in one of them, an emulsion (A), and, in another, a composition (B) comprising one or more alkaline agents.
