In an apparatus for building tires for vehicle wheels, a forming drum is loaded on a shuttle movable on a guide along a deposition line. The shuttle is moved on the guide in the two running directions to bring it to dispensing stations of semifinished products disposed in at least some deposition locations positioned in space succession along the deposition line. At each of the dispensing stations, at least one semifinished product is laid on a radially external surface to the forming drum carried by the shuttle for forming at least one component of a tire. The shuttle is moved on the guide in a different sequence from the space succession of the deposition locations along the deposition line.