A pneumatic vehicle tire having a belt and a radial carcass. Located laterally outwardly in the bead region are end portions of the carcass ply or plies which are guided upwardly, i.e. radially outwardly. Bead reinforcers are also provided. In order to achieve a great dynamic resilience along with sufficient stiffness of the bead regions, it is proposed pursuant to the present invention that the filaments of the bead reinforcers, and the strength carriers of the end portions of the carcass, be disposed at opposite inclines relative to the radial direction. Furthermore, in the vicinity of their outer ends, these filaments and strength carriers form a smaller angle with the circumferential direction of the tire than do those portions thereof in the bead core region, so that these reinforcing inserts are thus disposed in such a way that they extend in a curved manner.