The invention relates to a foaming cleanser cosmetic composition containing, in a physiologically acceptable medium: —a surfactant system comprising (i) at least one N—(C6-C30)acyl-amino based surfactant and (ii) at least one amphoteric surfactant chosen from betaines or (C8-C20)alkyl betaines, (C8-C20)alkylamido(C1-C6)alkylbetaines and mixtures thereof； and—at least one non associative crosslinked copolymer or acrylic acid and/or methacrylic acid, and optionally of (C1-C4)alkyl esters thereof, wherein said N—(C6-C30)acyl-amino based surfactant being present in the surfactant system in a major weight amount, and the surfactant system being present in the composition in an amount of less than 15% by weight relative to the total weight of the composition. The invention also relates to a process for cleansing keratin materials, which consists in applying the said composition to the said keratin materials, in working it into a foam and then in rinsing off the said composition, as well as 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.
