Composition with non-silicone elastomer and pasty fatty substance

A cosmetic composition comprising, in a physiologically acceptable medium:

• a cross-linked polyurethane elastomer gel comprising
• a single crosslinked polyurethane elastomer (copolymer) or a mixture of at least two crosslinked polyurethane elastomers (copolymers), said copolymer or said mixture of copolymers being obtained from a prepolymer having at least two hydroxyl groups and a (poly)isocyanate and at least one solvent, at least one polyol and a diisocyanate, and
• one or more pasty fatty substances selected from the group consisting of:
• (i) esters of polyol(s) and fatty acid diacid dimer, or an ester thereof,
• (ii) hydrogenated castor oil esters,
• (iii) oligomeric esters of glycerol,
• (iv) and mixtures thereof
• wherein the prepolymer having at least two hydroxyl groups is a copolymer of a C12-C18 fatty acid dimer, and a polyol selected from the group consisting of an aliphatic diol having 2 to 8 carbon atoms, and wherein the (poly)isocyanate is a diisocyanate.