The present invention provides a cosmetic composition comprising, in a cosmetically acceptable organic liquid medium, at least one film-forming ethylenic linear block polymer, and another film former. The film former may be soluble or dispersible in the said organic liquid medium. The composition may include an aqueous phase, in which case the film former may be soluble or dispersible in the aqueous phase. The invention further provides for the use of the combination of such a block polymer and a film former for enhancing the staying power of the said composition on the keratin materials.