Cosmetic composition comprising: i) at least one direct dye bearing a disulfide function, a thiol function or a protected-thiol function, of formula: A- p -C sat -S-U salts thereof with an organic or mineral acid, optical or geometric isomers thereof, tautomers thereof, and solvates thereof such as the hydrates, in which formula: • U represents a radical chosen from: a) -S-C' sat -(X') p '-A'; and b) - Y; • A and A', which may be identical or different, represent a radical containing at least one quaternized cationic chromophore or at least one chromophore bearing a quaternized or quaternizable cationic group; • Y represents i) a hydrogen atom; or ii) a thiol-function protecting group; • X and X', which may be identical or different, represent a linear or branched, saturated or unsaturated divalent C 1 -C 30 hydrocarbon-based chain, optionally interrupted and/or optionally terminated at one or both of its ends with one or more divalent groups or combinations thereof chosen from: -N -, -N + -, -O-, -S-, -CO-, -SO 2 - with R, which may be identical or different, chosen from a hydrogen and a C 1 -C 4 alkyl, hydroxyalkyl or aminoalkyl radical; an aromatic or non-aromatic, saturated or unsaturated, fused or non-fused (hetero)cyclic radical optionally comprising one or more identical or different, optionally substituted heteroatoms; • p and p', which may be identical or different, are equal to 0 or 1; • C sat and C' sat, which may be identical or different, represent an optionally cyclic, optionally substituted linear or branched C 1 -C 18 alkylene chain; ii) at least one nonionic surfactant; iii) at least one amphoteric surfactant; iv) at least one alkaline agent; and v) at least one reducing agent. i) at least one direct dye bearing a disulfide function, a thiol function or a protected-thiol function, of formula: A- p -C sat -S-U salts thereof with an organic or mineral acid, optical or geometric isomers thereof, tautomers thereof, and solvates thereof such as the hydrates, in which formula: • U represents a radical chosen from: a) -S-C' sat -(X') p '-A'; and b) - Y; • A and A', which may be identical or different, represent a radical containing at least one quaternized cationic chromophore or at least one chromophore bearing a quaternized or quaternizable cationic group; • Y represents i) a hydrogen atom; or ii) a thiol-function protecting group; • X and X', which may be identical or different, represent a linear or branched, saturated or unsaturated divalent C 1 -C 30 hydrocarbon-based chain, optionally interrupted and/or optionally terminated at one or both of its ends with one or more divalent groups or combinations thereof chosen from: -N -, -N + -, -O-, -S-, -CO-, -SO 2 - with R, which may be identical or different, chosen from a hydrogen and a C 1 -C 4 alkyl, hydroxyalkyl or aminoalkyl radical; an aromatic or non-aromatic, saturated or unsaturated, fused or non-fused (hetero)cyclic radical optionally comprising one or more identical or different, optionally substituted heteroatoms; • p and p', which may be identical or different, are equal to 0 or 1; • C sat and C' sat, which may be identical or different, represent an optionally cyclic, optionally substituted linear or branched C 1 -C 18 alkylene chain; • U represents a radical chosen from: a) -S-C' sat -(X') p '-A'; and b) - Y; a) -S-C' sat -(X') p '-A'; and b) - Y; • A and A', which may be identical or different, represent a radical containing at least one quaternized cationic chromophore or at least one chromophore bearing a quaternized or quaternizable cationic group; • Y represents i) a hydrogen atom; or ii) a thiol-function protecting group; • X and X', which may be identical or different, represent a linear or branched, saturated or unsaturated divalent C 1 -C 30 hydrocarbon-based chain, optionally interrupted and/or optionally terminated at one or both of its ends with one or more divalent groups or combinations thereof chosen from: -N -, -N + -, -O-, -S-, -CO-, -SO 2 - with R, which may be identical or different, chosen from a hydrogen and a C 1 -C 4 alkyl, hydroxyalkyl or aminoalkyl radical; an aromatic or non-aromatic, saturated or unsaturated, fused or non-fused (hetero)cyclic radical optionally comprising one or more identical or different, optionally substituted heteroatoms; -N -, -N + -, -O-, -S-, -CO-, -SO 2 - with R, which may be identical or different, chosen from a hydrogen and a C 1 -C 4 alkyl, hydroxyalkyl or aminoalkyl radical; an aromatic or non-aromatic, saturated or unsaturated, fused or non-fused (hetero)cyclic radical optionally comprising one or more identical or different, optionally substituted heteroatoms; • p and p', which may be identical or different, are equal to 0 or 1; • C sat and C' sat, which may be identical or different, represent an optionally cyclic, optionally substituted linear or branched C 1 -C 18 alkylene chain; ii) at least one nonionic surfactant; iii) at least one amphoteric surfactant; iv) at least one alkaline agent; and v) at least one reducing agent.