According to a first aspect, the present invention relates to a composition containing: a) an aqueous phase, b) an oily phase comprising at least one nonvolatile hydrocarbon-based oil chosen from linear or branched hydrocarbons； c) at least one surfactant of the N-acylsarcosinate type and d) at least one amphoteric or zwitterionic surfactant, and e) at least 6.50% by weight, relative to the total weight of the composition, of at least one structuring agent chosen from saturated fatty acids with a melting point of less than 45.0°C, saturated fatty alcohols with a melting point of less than 45.0°C and mixtures thereof. Another subject of the invention is the cosmetic use of the composition as defined according to the present invention, as a product for cleansing and/or removing makeup from keratin materials. Another subject of the invention consists of a cosmetic process for cleansing grime from human keratin materials, characterized in that the composition of the invention is applied to said keratin materials in the presence of water, it is massaged to form a foam, and the foam formed and the grime are removed by rinsing with water.
