The present invention relates to a volatile oily composition comprising, andpreferably consisting of, from 50 to100% by weight of a mixture of paraffins and from 0 to 50% by weight of atleast one non-volatile oil. It also relates to the cosmeticcompositions containing the abovementioned oily composition, and the cosmeticuses of said cosmetic compositions, particularlyfor making up and/or caring for and/or protecting skin, lips, eyelashes and/ornails, and in antiperspirant / deodorant compositions.