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 and possibly 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.