Tyre for vehicle wheels, comprising at least one element made of crosslinked elastomeric material, in which said element includes an elastomeric composition comprising: (a) at least one elastomeric homopolymer or copolymer of 1,3-butadiene; (b) at least one copolymer of ethylene with at least one aromatic null-olefin, said copolymer being essentially free of side chains containing ethylenic double bonds. Preferably, said element including said composition is a tread band of the tyre. The above (mentioned elastomeric composition makes it possible to prepare tread bands having both a low rolling resistance at the normal working temperatures of the tyre (40null C.-70null C.) and a high roadholding when the tread band is thermally stressed above these temperatures.