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.
