Process for building tyres, wherein: in a shaping station, a toroidal forming drum is positioned within a carcass sleeve comprising at least one carcass ply associated with a pair of beads, the toroidal forming drum comprising radially movable circumferentially consecutive sectors, wherein each sector has circumferentially opposite coupling portions (36a, 36b), each comprising elongated protrusions alternating with circumferentially elongated cavities, wherein the protrusions of each sector are slidably engaged in the respective cavities of circumferentially adjacent sectors; in the shaping station, the carcass sleeve is engaged by gripping elements (16a, 16b) operating axially and/or radially inside the beads; the carcass sleeve is toroidally shaped by radial expansion of the forming drum; the gripping elements (16a, 16b) disengage the beads during the expansion of the forming drum, after a radially outer portion of the forming drum has abutted against the carcass sleeve; the forming drum carrying the shaped carcass sleeve is removed from the shaping station; tyre components (7, 8, 9) are applied externally on the shaped carcass sleeve carried by the forming drum, wherein at least one of said tyre components (7, 8, 9) comprises at least one sidewall portion having a radially inner apex joining with one of said beads and being made by wrapping at least one elongated continuous element (47a, 54) according to circumferential turns (C, C1) axially side by side around a radially outer surface of the carcass sleeve coupled to the forming drum; wherein at the end of the shaping of the carcass sleeve and during the application of said tyre components (7, 8, 9), axially inner sides of said beads are entirely arranged in axial abutment relation against respective circumferential axially outer portions of an abutment surface carried by the expanded forming drum, said expanded forming drum having a toroidal shape corresponding to an inner shape of the shaped carcass sleeve. in a shaping station, a toroidal forming drum is positioned within a carcass sleeve comprising at least one carcass ply associated with a pair of beads, the toroidal forming drum comprising radially movable circumferentially consecutive sectors, wherein each sector has circumferentially opposite coupling portions (36a, 36b), each comprising elongated protrusions alternating with circumferentially elongated cavities, wherein the protrusions of each sector are slidably engaged in the respective cavities of circumferentially adjacent sectors; in the shaping station, the carcass sleeve is engaged by gripping elements (16a, 16b) operating axially and/or radially inside the beads; the carcass sleeve is toroidally shaped by radial expansion of the forming drum; the gripping elements (16a, 16b) disengage the beads during the expansion of the forming drum, after a radially outer portion of the forming drum has abutted against the carcass sleeve; the forming drum carrying the shaped carcass sleeve is removed from the shaping station; tyre components (7, 8, 9) are applied externally on the shaped carcass sleeve carried by the forming drum, wherein at least one of said tyre components (7, 8, 9) comprises at least one sidewall portion having a radially inner apex joining with one of said beads and being made by wrapping at least one elongated continuous element (47a, 54) according to circumferential turns (C, C1) axially side by side around a radially outer surface of the carcass sleeve coupled to the forming drum; wherein at the end of the shaping of the carcass sleeve and during the application of said tyre components (7, 8, 9), axially inner sides of said beads are entirely arranged in axial abutment relation against respective circumferential axially outer portions of an abutment surface carried by the expanded forming drum, said expanded forming drum having a toroidal shape corresponding to an inner shape of the shaped carcass sleeve.