The disclosure relates to a composition for dyeing keratin fibers, in particular human keratin fibers such as hair, comprising one or more oxidation dyes, one or more scleroglucan gums in a total weight content greater than or equal to 0.5% relative to the total weight of the composition, and one or more and optionally one or more additional surfactants, preferably cationic surfactants. The disclosure also relates to a method for dyeing keratin fibers using said composition and to a multi-compartment device suitable for implementing said composition.