To obtain a composition for local application resistant to friction and sebum and having excellent sustaining power without movement and transfer by including a fatty phase and a film-forming polymer in a support.

This composition is obtained by including (A) at least one fatty phase and (B) at least one film-forming polymer in a physiologically acceptable support. The ingredient A contains at least one fatty substance selected from a 4C hydrocarbon wax and oil, a 7C compound containing at least one C-O bond, a silicone oil, a fluorinatd oil and a mixture thereof and the ingredient B is an optionally substituted poly(hydroxystyrene). When the oil contains at least one C-O bond and is selected from at least the 7C compound, the weight ratio of the oil to the poly(hydroxystyrene) is ≥0.5.