This invention relates to a composition comprising at least the following in a physiologically acceptable medium:an aqueous phase and；an oily phase comprising at least one non-volatile hydrocarbon oil chosen from among linear or branched hydrocarbons, and；at least one glycinate type anionic surfactant andpossibly at least one additional anionic surfactant different from glycinates and fatty acid salts；at least one amphoteric or zwitterionic surfactant and；at least 5% by weight of the total weight of the composition of at least one structuring agent chosen from among saturated fatty acids with a melting point of less than 45° C., saturated fatty alcohols with a melting point of less than 45° C., and mixtures thereof and；the ratio by weight of the total quantity of anionic surfactants and amphoteric or zwitterionic surfactants to the quantity of the structuring agent varies between 80/20 and 60/40.
