The invention relates to a composition in the form of a nanoemulsion or micro-emulsion, comprising: at least two different fatty acid esters of (poly)glycerol a) and b); c) at least one polyol in a total content of greater than 15% by weight; d) at least one oil; e) water; and f) at least one anionic surfactant of formula (II) it being understood that said composition comprises at least one anionic surfactant of formula (II) when the first fatty acid ester of (poly)glycerol is a polyglyceryl laurate comprising from 3 to 6 glycerol units and the second fatty acid ester of (poly)glycerol is a (poly)glyceryl laurate comprising from 1 to 3 glycerol units. The invention also relates to a cosmetic treatment process for reducing and/or preventing the signs of ageing of keratin materials such as the skin, by application of such a composition.