Composition comprises at least one fatty substance, surfactant, oxidation base comprising heterocyclic oxidation bases, alkalinizing agent and coupler having amine compounds (I), where the fatty substances are present at at least 25 wt.%. Composition comprises at least one fatty substance, surfactant, oxidation base comprising heterocyclic oxidation bases, alkalinizing agent, coupler having amine compounds of formula (I) and their salts, optical and geometric isomers and tautomers or hydrates, where the fatty substances are present at at least 25 wt.%. R1 : H (preferred), linear 1-10C alkyl or 2-10C alkenyl radical, branched 3-10C alkyl or 3-10C alkenyl, or 3-8 membered cyclic alkyl or alkenyl radical optionally comprising one or more unsaturations, preferably CH 3, where one or more of the carbon atoms of the alkyl or alkenyl radical are possibly replaced with at least one of O, N or S, or with SO 2, and the alkyl or alkenyl radical is optionally substituted； either R2 : linear 2-10C or branched 3-10C alkenyl radical, linear 1-10C or branched 3-8C alkyl radical (both optionally substituted), OH, halo, carboxyl or (1-8C)alkoxycarbonyl, where the radical R2 is connected to the heterocycle via a carbon-carbon single bond； or R2R2+adjacent carbon atoms : 5-8 membered ring (optionally substituted)； or R2R2+same carbon atom : =CH-R1a； R1a : H or linear 1-9C or branched 3-9C alkyl； n : 0-4, preferably 0-2, provided that when n is less than 4, the unsubstituted carbon atoms comprise one or more H； R3 : linear 1-10C or branched 3-8C alkyl radical, linear 2-10C or branched 3-10C alkenyl radical (both optionally substituted), halo, OH (preferred), 1-8C alkoxy optionally carrying OH group, 1-8C alkylthio, NH 2, mono- or di-alkylamino, 1-8C alkyl optionally bearing OH group, -NH-CO-NHR2a or -SR4； R2a, R4 : H or 1-4C alkyl； and p : 0-3, preferably 0 or 1, provided that when p is less than 3, the unsubstituted carbon atoms are H. Independent claims are included for: (1) dyeing ke
