A process and a drum for looping annular anchoring structures in a process for building tyres for vehicle wheels includes: depositing a loop on a drum including a radially expandable/contractible intermediate annular portion and, in a position axially adjacent to the opposite axial ends of said intermediate annular portion, a pair of radially expandable/contractible lateral annular portions; associating an annular anchoring structure with a radially outer annular surface portion of the loop defined at the intermediate annular portion; and turning up each of opposite end edges of the loop on the annular anchoring structure through the lateral annular portions as a result of a thrusting stress imparted by a respective lateral annular portion of said pair of lateral annular portions because of a synchronous radial movement and a synchronous axial displacement of a respective plurality of circumferentially adjacent first angular sectors.