The invention relates to a cosmetic composition comprising: one or more linear α-olefin sulfonates, one or more anionic surfactants present in the composition in an amount ranging from 1% to 20% by weight; and one or more additional surfactants chosen from amphoteric surfactants and nonionic surfactants, the weight ratio of the amount of linear α-olefin sulfonates to the amount of anionic surfactants being greater than or equal to 1. The invention also relates to a cosmetic treatment process using said composition, especially a process for caring for and/or cleansing keratin materials.