The invention relates to a physiologically acceptable composition, especially a cosmetic composition, comprising at least one volatile solvent and a liquid fatty phase comprising at least one structuring polymer, said structuring polymer (homopolymer or copolymer) having an average molecular weight of from 500 to 500,000 and comprising at least one moiety which comprises: at least one polyorganosiloxane group consisting of 1 to 1000 organosiloxane units in the chain of the moiety or in the form of 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° C.
