A run-flat tire system comprising a tire and an tire core disposed therein, the tire core being an annular body of an elastic closed-cell material, the radially outside and inside of the tire core each provided with a circumferentially extending groove, the radially inner groove extending radially outwardly beyond a bead core line being drawn between the centers of the bead cores. When the tire is mounted on a standard rim, the radially outer groove forms a radially outer space extending circumferentially of the tire and having a cross sectional area of from 1 to 6% of the total sectional area of the tire cavity, and the radially inner groove forms a radially inner space extending circumferentially of the tire having a cross sectional area Si of from 10 to 25% of the total sectional area S of the tire cavity.