The invention relates to a physiologically acceptable composition, in particular a cosmetic composition, containing at least one liquid fatty phase comprising at least one structuring polymer comprising a polymer skeleton having hydrocarbon-based repeating units containing at least one hetero atom, and and at least one gelling agent for the said fatty phase, the liquid fatty phase, the structuring polymer and the gelling agent forming a physiologically acceptable medium. This composition may be in the form of a stick of lipstick which is stable, which does not exude and whose application produces a glossy deposit with good staying power over time.