The present invention relates to a solid anhydrous composition for caring for and/or making up keratin materials comprising, a) greater than or equal to 5 ％ of at least one oil chosen from fatty acid triglycerides, relative to the total weight of the composition, b) at least one pasty compound chosen from an ester of dimer dilinoleic acid and polyol (s) or an ester thereof, and c) at least one wax of solid linear ester derived from C6-C30 fatty acid. The present invention also relates to a process for caring for and/or making up keratin materials such as the skin and the lips, preferably the lips, by applying the solid anhydrous composition according to the present invention to the keratin materials.
