A plant and a process for building green tyres for vehicle wheels. The process includes: a) building a carcass structure on a first forming drum in at least one carcass structure building line including a plurality of work stations arranged according to a sequential series, the carcass structure including at least one carcass ply and a pair of annular anchoring structures; b) building a crown structure on at least one second forming drum in at least one crown structure building line including a plurality of work stations arranged according to a sequential series, the crown structure including at least one belt structure; c) toroidally shaping the carcass structure assembling it to the crown structure in at least one shaping and assembling work station, wherein the transfers of each of the first forming drum and the second forming drum, with the respective carcass structure and crown structure being processed, from one work station to the other of the respective building lines includes at least one transfer from a first work station to a second work station not adjacent to the first one in the sequential series, and wherein each step d) of transfer takes place in such a way that the first forming drum and the second forming drum only pass in the first and second work station.