A process for straightening or relaxing hair comprising the following steps: (a) providing a hair straightening or relaxing composition having a pH ranging from 8 to 11.5, and containing, in a cosmetically acceptable medium, at least one weak acid chosen from monocarboxylic, dicarboxylic and tricarboxylic acids, their salts, and mixtures thereof (b) contacting the hair with the hair straightening or relaxing composition to form treated hair and (c) straightening or relaxing the treated hair by applying heat, wherein hydroxide-containing compounds are not used. Disclosed herein is also a preferred hair straightening or relaxing composition.
