The present invention relates to a composition containing in an aqueous medium, at least: 1) an internal olefin sulfonate composition comprising: (A) an internal olefin sulfonate having 16 carbon atoms and (B) an internal olefin sulfonate having 18 carbon atoms, wherein a mass content ratio (A/B) of the component (A) to the component (B) contained in the sulfonate composition ton is from 75/25 to 90/10, and wherein a mass ratio (hydroxy form/olefin form) of a content of a hydroxy form in the internal olefin sulfonate of the component (A) and the component (B) to a content of an olefin form in the internal olefin sulfonate of the component (A) and the component (B) is from 75/25 to 100/0 and 2) at least one polymeric suspension agent. The present invention relates also to a process for cleansing keratin materials, which consists of applying to the said keratin materials a composition according to the invention, in working the said composition into a foam and then rinsing off the said composition, especially with water. The present invention relates also to the cosmetic use of the composition as defined above, for removing makeup and/or cleansing the skin, the hair and/or mucous membranes, or for skincare.
