During building of a tyre, at least one component of elastomeric material is manufactured through application of an elongated element in the form of coils disposed side by side and/or superposed onto a forming support driven in rotation and transversely moved in front of an applicator device. The elongated element is formed by feeding a continuous thread element coming from an extruder between two shaping rollers. During formation, a detector operating close to the shaping rollers cyclically detects the width of the elongated element and the cross-section area of the continuous thread element to monitor the volumetric flow rate of the continuous thread element close to the shaping rollers. The feeding speed of the continuous thread element toward the shaping rollers is adjusted through feedback on the extruder or on a driving device operating downstream of the extruder itself, to keep the volumetric flow rate value within a predetermined range.