An apparatus for building tyres for vehicle wheels includes a building drum having at least one first outer circumferential surface, and at least one pair of auxiliary support members removably in engagement with the building drum, each in axial side by side relationship with a respective end of the building drum and having second outer circumferential surfaces extending in the continuation of the first outer circumferential surface so as to support at least one component of the tyre. Each of the second outer circumferential surfaces has at least one non-stick circumferential portion and at least one sticking circumferential portion.