The present invention relates to a cosmetic composition including, in a physiologically acceptable medium: (a) at least 30% by weight of an anhydrous gel having a viscosity of at least 180 000 cP-s at 25° C. which includes at least one oil and at least one copolymer of styrene and at least one olefin other than styrene (b) at least one specific glycerol diester and (c) optionally at most 10% by weight of wax(es), the composition exhibiting a phase shift δ between its elastic modulus (G′) and its viscous modulus (G′) of less than 45° at a frequency of 30 to 50 Hz. It also relates to a cosmetic method for caring for or making up the lips, including the topical application to the lips of the abovementioned composition.
