An apparatus for looping anchoring annular structures of a tyre for vehicle wheels, includes at least three looping drums. Each looping drum has a longitudinal axis thereof, with respect to which it is radially expandable/contractible in a manner so as to turn up the loop around an anchoring annular structure. The apparatus also includes a loop deposit station, a loading station configured for loading the anchoring annular structures on the looping drum and an unloading station configured for unloading the looped anchoring annular structures from the looping drum. The loop deposit station, loading station and unloading station are angularly offset from each other. A turret transfer apparatus supports the looping drums in positions angularly offset with respect to each other and is configured for transferring the looping drums between the loop deposit station, the loading station and the unloading station rotating around a vertically-arranged transfer axis.