Process for relaxing keratin fibres, comprising: (i) a step of applying to the keratin fibres a hair-relaxing composition having a pH of less than 9 and containing at least two denaturing agents, - at least one of the denaturing agents is a guanidine corresponding to the general formula below: in which: R1, R2, R3, R4 and R5 represent, independently: (i) a hydrogen atom or (ii) a linear or branched C1-C4 lower alkyl or alkenyl radical, optionally substituted with one or two radicals chosen from: hydroxyl, amino, dimethylamino, methoxy, ethoxy, carboxyl, carboxamide, N-methyl-carboxamide or SO 3 H, and the organic or mineral salts thereof, - and at least one denaturing agent chosen from the α-keto acid derivatives corresponding to the general formula: - R5 represents COOH, a linear or branched C1-C6 alkyl optionally substituted with an OH, COOH or Br radical; a phenyl or benzyl optionally substituted with an OH or COOH radical; or alternatively an indolyl radical or - and the stereoisomers, organic or mineral salts and solvates thereof, (ii) a step of raising the temperature of the keratin fibres, using a heating means, to a temperature of between 110 and 250°C. (i) a step of applying to the keratin fibres a hair-relaxing composition having a pH of less than 9 and containing at least two denaturing agents, - at least one of the denaturing agents is a guanidine corresponding to the general formula below: in which: R1, R2, R3, R4 and R5 represent, independently: (i) a hydrogen atom or (ii) a linear or branched C1-C4 lower alkyl or alkenyl radical, optionally substituted with one or two radicals chosen from: hydroxyl, amino, dimethylamino, methoxy, ethoxy, carboxyl, carboxamide, N-methyl-carboxamide or SO 3 H, and the organic or mineral salts thereof, - and at least one denaturing agent chosen from the α-keto acid derivatives corresponding to the general formula: - R5 represents COOH, a linear or branched C1-C6 alkyl optionally substituted with an OH, COOH or Br radical; a phenyl or benzyl optionally substituted with an OH or COOH radical; or alternatively an indolyl radical or - and the stereoisomers, organic or mineral salts and solvates thereof, - at least one of the denaturing agents is a guanidine corresponding to the general formula below: in which: R1, R2, R3, R4 and R5 represent, independently: (i) a hydrogen atom or (ii) a linear or branched C1-C4 lower alkyl or alkenyl radical, optionally substituted with one or two radicals chosen from: hydroxyl, amino, dimethylamino, methoxy, ethoxy, carboxyl, carboxamide, N-methyl-carboxamide or SO 3 H, and the organic or mineral salts thereof, R1, R2, R3, R4 and R5 represent, independently: (i) a hydrogen atom or (ii) a linear or branched C1-C4 lower alkyl or alkenyl radical, optionally substituted with one or two radicals chosen from: hydroxyl, amino, dimethylamino, methoxy, ethoxy, carboxyl, carboxamide, N-methyl-carboxamide or SO 3 H, (i) a hydrogen atom or (ii) a linear or branched C1-C4 lower alkyl or alkenyl radical, optionally substituted with one or two radicals chosen from: hydroxyl, amino, dimethylamino, methoxy, ethoxy, carboxyl, carboxamide, N-methyl-carboxamide or SO 3 H, and the organic or mineral salts thereof, - and at least one denaturing agent chosen from the α-keto acid derivatives corresponding to the general formula: - R5 represents COOH, a linear or branched C1-C6 alkyl optionally substituted with an OH, COOH or Br radical; a phenyl or benzyl optionally substituted with an OH or COOH radical; or alternatively an indolyl radical or - and the stereoisomers, organic or mineral salts and solvates thereof, (ii) a step of raising the temperature of the keratin fibres, using a heating means, to a temperature of between 110 and 250°C.