A run-flat tire comprising a carcass structure having opposite lateral edges associated with respective right-hand and left-hand bead structures; a tread band applied in a radially external position with respect to said carcass structure; a pair of sidewalls applied laterally on opposite sides with respect to said carcass structure; a bearing structure including for each side of the tire said bead structure cooperating in supporting the run-flat tire with at least one sidewall insert extending radially between said bead structure and the corresponding lateral edge of said tread band; a bearing structure including, for each side of the tire, said bead structure cooperating in supporting the run- flat tire with at least one sidewall insert extending radially between said bead structure and the corresponding lateral edge of said tread band, wherein said at least one sidewall insert includes a crosslinked elastomeric material obtained by crosslinking a crosslinkable elastomeric composition comprising: (a) 100 phr of at least one elastomeric polymer; (b) from about 20 phr to about 35 phr, preferably from about 20 phr to about 25 phr of diatomite particles having a BET surface area, in the range of from about 10 m2/g to about 90 m 2 /g, preferably from about 10 to about 40 m 2 /g, more preferably from about 30 to about 40 m 2 /g; (c) from about 10 phr to about 35 phr, preferably from about 25 phr to about 35 phr of at least one further reinforcing filler.