A pneumatic tyre for a two-wheeled vehicle includes a carcass structure, belt structure, tread band, and pair of sidewalls. The carcass structure includes at least one first and second carcass ply. Each carcass ply includes cords disposed substantially parallel to each other. Ends of each carcass ply are engaged with respective circumferential annular reinforcing structures. Each carcass ply cord identifies a radial plane of the tyre passing through an intersection point of the cord with an equatorial plane of the tyre and lies in a plane substantially perpendicular to the equatorial plane and forming a lying angle different from zero with a respective radial plane. The lying angle of each cord of the at least one first carcass ply and the lying angle of a corresponding cord of the at least one second carcass ply identifying a same radial plane have opposite signs with respect to that radial plane.