The present invention relates to a method for loosening loops and / or smoothing keratinous fibers, in particular keratin fibers such as the hair, comprising: • either: i) the application on said fibers of an (A) acidic composition preferably having a pH of from 1 to 5 inclusive and containing one or more thiol reducing agents in an amount of less than 8% by weight based on the total weight of the composition (A)； ii) applying to said fibers a separate composition (B) containing one or more compounds of formula (I): RO-C (O) -ALK-C (O) -OR, wherein ALK, R and R ', are as defined in the description； Or (iii) the application of an acidic composition (D) containing: a) one or more thiolated reducing agents in an amount of less than 8% by weight relative to the total weight of the composition (D)； and b) one or more compounds of formula (I) as defined above； followed iv) a heat treatment step of the fibers by means of a heating tool； it being understood that: - steps i) and ii) can be applied together or separately, preferably together, - steps i) and ii) are followed by step iv) of heat treatment or step iii) is followed by step iv) heat treatment. The subject of the invention is also the use of the composition (A), (B) or (D) for relaxing loops and / or for smoothing keratinous fibers, a composition (D) and a device with several compartments or "Kit" suitable for the implementation of such a method. La présente invention concerne un procédé de détente de boucles et/ou de lissage des fibres kératiniques, en particulier des fibres kératiniques telles que les cheveux, comprenant : • Soit : i) l'application sur lesdites fibres d'une composition (A) acide, de préférence ayant un pH compris inclusivement entre 1 et 5 et contenant un ou plusieurs agents réducteurs thiolés en quantité inférieure à 8 % en poids par rapport au poids total de la composition (A) ； ii) l'application sur lesdites fibres d'une composition (B) distincte contenant un ou plusieurs c
