The present invention relates to a cosmetic make-up or care composition comprising an oily phase comprising at least one liquid polyester obtained by condensation of unsaturated fatty acid dimer and/or trimer and diol, said composition being free from lipophilic gelling agent or comprising at the most 10 wt.% thereof, relative to the weight of the composition. The present invention also relates to a method of make-up of the face and body comprising the use of said composition.
