A process for building tyres for vehicle wheels, comprising: forming at least one component of the tyre on a forming drum, wherein said component is formed by: - feeding a rubber-coated ribbon onto a conveyor along a feeding direction coincident with a longitudinal extension direction of said rubber-coated ribbon, until exceeding a cutting region of said conveyor by a predetermined length; the rubber-coated ribbon comprising a plurality of parallel reinforcing cords, embedded in a matrix of elastomeric material and inclined by a predetermined angle (α) relative to the longitudinal extension direction; - lifting a locating element placed under the rubber-coated ribbon and at the cutting region until lifting of the rubber-coated ribbon occurs; - moving a knife, placed upon the rubber-coated ribbon and at the cutting region, along a cutting direction, for engraving and cutting the rubber-coated ribbon between two adjacent reinforcing cords and over the whole width thereof so as to form a segment; - laying the segment on the forming drum; wherein, before the cut, a first portion of the rubber-coated ribbon placed upstream of the locating element is moved forward by a predetermined stretch (d), so as to reduce the tension of said rubber-coated ribbon caused by lifting of the locating element, wherein, during said moving forward, the rubber-coated ribbon rolls on at least one roller belonging to the locating element. forming at least one component of the tyre on a forming drum, wherein said component is formed by: - feeding a rubber-coated ribbon onto a conveyor along a feeding direction coincident with a longitudinal extension direction of said rubber-coated ribbon, until exceeding a cutting region of said conveyor by a predetermined length; the rubber-coated ribbon comprising a plurality of parallel reinforcing cords, embedded in a matrix of elastomeric material and inclined by a predetermined angle (α) relative to the longitudinal extension direction; - lifting a locating element placed under the rubber-coated ribbon and at the cutting region until lifting of the rubber-coated ribbon occurs; - moving a knife, placed upon the rubber-coated ribbon and at the cutting region, along a cutting direction, for engraving and cutting the rubber-coated ribbon between two adjacent reinforcing cords and over the whole width thereof so as to form a segment; - laying the segment on the forming drum; - feeding a rubber-coated ribbon onto a conveyor along a feeding direction coincident with a longitudinal extension direction of said rubber-coated ribbon, until exceeding a cutting region of said conveyor by a predetermined length; the rubber-coated ribbon comprising a plurality of parallel reinforcing cords, embedded in a matrix of elastomeric material and inclined by a predetermined angle (α) relative to the longitudinal extension direction; - lifting a locating element placed under the rubber-coated ribbon and at the cutting region until lifting of the rubber-coated ribbon occurs; - moving a knife, placed upon the rubber-coated ribbon and at the cutting region, along a cutting direction, for engraving and cutting the rubber-coated ribbon between two adjacent reinforcing cords and over the whole width thereof so as to form a segment; - laying the segment on the forming drum; wherein, before the cut, a first portion of the rubber-coated ribbon placed upstream of the locating element is moved forward by a predetermined stretch (d), so as to reduce the tension of said rubber-coated ribbon caused by lifting of the locating element, wherein, during said moving forward, the rubber-coated ribbon rolls on at least one roller belonging to the locating element.