A crosslinkable elastomeric composition includes an elastomeric polymer containing carboxylic groups and an epoxidized liquid organic compound containing epoxide groups located internally on a molecule of the organic compound. The composition is crosslinkable substantially in an absence of additional crosslinking agents. A process for producing tyres for vehicle wheels including the composition, a tyre for vehicle wheels including the composition, a tyre for vehicles with a tread band including the composition, and a crosslinked elastomeric product obtained by crosslinking the composition are also disclosed.