The invention relates to a composition comprising a physiologically acceptable medium containing a fatty phase comprising at least one ester resulting from the reaction of a polyol with a carboxylic acid of formula (I) below: in which R1, R2 and R3 are radicals independently chosen from optionally functionalized alkyl, aryl and aralkyl radicals, and combinations thereof. The invention also relates to the use of an ester of formula (I) above in a cosmetic composition with staying power properties, especially of the colour, and/or gloss and/or comfort and/or migration resistance properties.