A process for manufacturing tyres for vehicle wheels includes associating at least one reinforcing structure with at least one surface portion of at least one tyre component laid on a forming support, wherein associating the at least one reinforcing structure includes bringing, through a handling and deposition member, at least one reinforcing element to the forming support and depositing, through said handling and deposition member, the reinforcing element on a respective deposition part defined on a surface portion of the component. The depositing includes gradually laying the reinforcing element on the deposition part following the profile of the deposition part in a circumferential direction.