Coloring composition for dyeing the keratinous fibers comprises an oxidation dye precursor and/or a direct dye, a fatty alcohol, fatty acid ester of 1-10C alcohol, nonionic and/or anionic surface-active agents, a nonionic associated polymer, and water (at least 55 wt.%). Independent claims are included for: (1) a process of coloring keratinous fibers comprising, application of dry or wet coloring composition to the fibers; and (2) a device with several compartments for coloring the keratinous fibers, comprising a first compartment containing the coloring composition and a second compartment containing an oxidizing composition.