A process and apparatus for manufacturing tyres for vehicle wheels includes the step of building, on a forming support, a belt structure including at least one reinforcing structure of the so-called zero-degree type. The reinforcing structure is formed by depositing a continuous elongated reinforcing element on a deposition surface arranged in a radially outer position with respect to the forming support. The aforementioned deposition includes the step of exerting, through at least one element made from magnetic material, a magnetic attraction on a portion of the continuous elongated reinforcing element arranged at at least one pressing member and moving said at least one pressing member toward the forming support until the continuous elongated reinforcing element is brought into contact with the deposition surface.