The present invention relates to a composition for dyeing keratin fibres, in particular keratin fibres such as the hair, comprising: a) at least one oxidation base 3-(2,5-diaminophenyl)-1-propanol and/or acid salts thereof or solvates thereof such as hydrates b) at least one coupler c) at least 10% by weight of the total weight of the composition of a fatty substance which is preferably liquid and non-silicone-based d) at least one nonionic surfactant chosen from alkyl(poly)glycoside surfactants, esters of oxyalkylenated sorbitan and fatty acids and oxyalkylenated fatty alcohols e) optionally at least one basifying agent and f) optionally at least one chemical oxidizing agent. The invention also relates to a process for dyeing keratin fibres such as the hair using the composition of the invention, and to a multi-compartment device for using the composition of the invention.
