During building of tyres, at least one first forming drum is employed which has a deposition surface and includes sectors radially movable relative to a geometric rotation axis, and circumferentially distributed one after the other. A plurality of strip-like elements is deposited in circumferential side by side relationship on the deposition surface set in the first deposition configuration, to form at least one component of at least one first crown structure. Setting of the deposition surface includes the actions of radially moving the sectors to give the deposition surface a predetermined diameter and carry out a relative movement between a central portion and axially external end portions of each sector to shape the deposition surface according to a predetermined curvature outline.