The present invention relates to a cosmetic composition which is preferentially anhydrous, comprising from 10% to 40% by weight of liquid fatty esters, at least 30% by weight of volatile oils other than the liquid fatty esters, and thickeners. The composition may also comprise particles that are insoluble in the medium, such as pigments or microcapsules. The invention also relates to a cosmetic treatment process, especially for caring for or conditioning the hair, using this composition, which is more particularly intended for curly or frizzy hair.
