The invention relates to a nail polish composition comprising at least one liquid organic phase comprising at least one volatile organic solvent, the liquid organic phase being structured by at least one polymer with a weight-average molecular mass of less than or equal to 100 000 comprising a) a polymer backbone having hydrocarbonaceous repeat units which are provided with at least one heteroatom and optionally b) optionally functionalized pendent and/or end fatty chains which have from 6 to 120 carbon atoms and which are bonded to these units. This composition is provided in particular in the form of a nail polish stick.