The present invention relates to a cosmetic composition comprising: a) one or more amphoteric or zwitterionic surfactants, b) one or more cationic surfactants, c) one or more sulfureous reducing agents, and d) one or more alkaline agents, the weight ratio between the total amount of the amphoteric or zwitterionic surfactant(s), on the one hand, and the total amount of the cationic surfactant(s), on the other hand, being greater than or equal to 1.2. The present invention also relates to processes using this composition. The invention also relates to the use of the composition according to the invention for relaxing the curls and/or reducing the volume of keratin fibres, preferably the hair.
