A cleansing composition based on oily substances, particularly for cleansing skin and/or hair and having excellent dermatological properties, is described. The composition is characterized in that it comprises one or more oily substances at a total concentration of between 10% and 90% by weight relative to the composition and one or more surfactants selected from the N-acylates of amino-acids, proteins, and peptides, in acid or neutralized form, at a total concentration within the range of between 2% and 80% by weight relative to the composition, and in that it is substantially anhydrous or has a water content no greater than 10% by weight.