Cosmetic composition comprising: i) one or more dicarbonyl compounds corresponding to formula below, and/or derivatives thereof and/or hydrates thereof and/or salts thereof, the derivatives being chosen from esters of the carboxyl group(s), amides of the carboxyl group(s), and (thio)acetals and hemi(thio)acetals of the carbonyl function(s) of the compounds of formula, in free form or optionally in the form of salts or of hydrates, preferably in free form or in the form of hydrates: in which formula: R represents an atom or group chosen from i) hydrogen, ii) carboxyl -C -OH, iii) linear or branched C 1 -C 6 alkyl which is optionally substituted, preferably with at least one hydroxyl -OH radical, carboxyl radical or halogen radical such as Br; iv) optionally substituted phenyl, v) optionally substituted benzyl, iv) and v) preferably being optionally substituted with at least one -OH or -C -OH radical; vi) an indolyl radical and vii) an imidazolylmethyl radical and its tautomers such as with * representing the part linked to the rest of the molecule; the dicarbonyl compounds corresponding to formula, and/or derivatives thereof and/or hydrates thereof and/or salts thereof being present in the composition in an amount ranging from 5 to 15 % in weight of the total weight of the composition; ii) one or more acids different from the compound(s) i) as defined previously; and iii) one or more alkalinizing agents chosen from i) aqueous ammonia, ii) alkali metal or alkaline-earth metal carbonates or hydrogen carbonates, such as sodium carbonates or hydrogen carbonates or potassium carbonates or hydrogen carbonates, iii) alkali metal or alkaline-earth metal phosphates or (di)hydrogen phosphates, iv) alkali metal or alkaline-earth metal hydroxides, such as sodium or potassium hydroxides, or mixtures thereof, v) alkanolamines, such as monoethanolamine or trihydroxyethylamine, vi) oxyethylenated and/or oxypropylenated ethylenediamines, vii) amino acids and viii) the compounds of formula below: in which formula W is a divalent C 1 -C 6 alkylene radical optionally substituted with one or more hydroxyl groups or a C 1 -C 6 alkyl radical, and/or optionally interrupted with one or more heteroatoms such as O, or NR u; R x, R y, R z, R t and R u, which may be identical or different, represent a hydrogen atom or a C 1 -C 6 alkyl, C 1 -C 6 hydroxyalkyl or C 1 -C 6 aminoalkyl radical; the said dicarbonyl compound(s) corresponding to formula being different from pyruvic acid, a derivative thereof and hydrates thereof or salts thereof - the derivatives being chosen from esters of the carboxyl group(s), amides of the carboxyl group(s), and (thio)acetals and hemi(thio)acetals of the carbonyl function(s) of the pyruvic acid in free form or in the form of hydrates. i) one or more dicarbonyl compounds corresponding to formula below, and/or derivatives thereof and/or hydrates thereof and/or salts thereof, the derivatives being chosen from esters of the carboxyl group(s), amides of the carboxyl group(s), and (thio)acetals and hemi(thio)acetals of the carbonyl function(s) of the compounds of formula, in free form or optionally in the form of salts or of hydrates, preferably in free form or in the form of hydrates: in which formula: R represents an atom or group chosen from i) hydrogen, ii) carboxyl -C -OH, iii) linear or branched C 1 -C 6 alkyl which is optionally substituted, preferably with at least one hydroxyl -OH radical, carboxyl radical or halogen radical such as Br; iv) optionally substituted phenyl, v) optionally substituted benzyl, iv) and v) preferably being optionally substituted with at least one -OH or -C -OH radical; vi) an indolyl radical and vii) an imidazolylmethyl radical and its tautomers such as with * representing the part linked to the rest of the molecule; the dicarbonyl compounds corresponding to formula, and/or derivatives thereof and/or hydrates thereof and/or salts thereof being present in the composition in an amount ranging from 5 to 15 % in weight of the total weight of the composition; ii) one or more acids different from the compound(s) i) as defined previously; and iii) one or more alkalinizing agents chosen from i) aqueous ammonia, ii) alkali metal or alkaline-earth metal carbonates or hydrogen carbonates, such as sodium carbonates or hydrogen carbonates or potassium carbonates or hydrogen carbonates, iii) alkali metal or alkaline-earth metal phosphates or (di)hydrogen phosphates, iv) alkali metal or alkaline-earth metal hydroxides, such as sodium or potassium hydroxides, or mixtures thereof, v) alkanolamines, such as monoethanolamine or trihydroxyethylamine, vi) oxyethylenated and/or oxypropylenated ethylenediamines, vii) amino acids and viii) the compounds of formula below: in which formula W is a divalent C 1 -C 6 alkylene radical optionally substituted with one or more hydroxyl groups or a C 1 -C 6 alkyl radical, and/or optionally interrupted with one or more heteroatoms such as O, or NR u; R x, R y, R z, R t and R u, which may be identical or different, represent a hydrogen atom or a C 1 -C 6 alkyl, C 1 -C 6 hydroxyalkyl or C 1 -C 6 aminoalkyl radical;