There are described a green tyre, a tyre, a process and a plant for building tyres. The process comprises building a carcass structure (110, 210) and a crown structure (130, 230) comprising a belt structure (140, 240) and a tread band (150, 250), and associating the carcass structure with the crown structure. The building of the crown structure envisages the building of the belt structure on a drum (520) and the deposition of the tread band in a position radially outside the belt structure. The deposition of the tread band comprises the provision of a predetermined elastomeric material (531) in a hot - extrusion device (530), the extrusion from the extrusion device of a band (531) of elastomeric material having a width equal to the predetermined width of the tread band and a thickness smaller than the predetermined thickness of the tread band, and the hot¢deposition of the band onto the belt structure in at least two overlapping layers.