A physiologically acceptable composition, especially a cosmetic composition, comprising a liquid fatty phase comprising at least one silicone oil, structured with at least one polymer chosen from homopolymers and copolymers with a weight-average molecular mass ranging from 500 to 500 000, comprising at least one moiety comprising: at least one polyorganosiloxane group comprising from 1 to 1 000 organosiloxane units in the chain of the moiety of in the form of a graft, and at least two groups capable of establishing hydrogen interactions, the polymer being solid at room temperature and soluble in the liquid fatty phase at a temperature of from 25 to 250.degree. C., and solid particles having a hydrophobic surface.