Abstract: A method and machine for producing a tyre component part by gradually depositing a strip of elastomeric material on a toroidal surface of a support rotating about its axis; the machine incorporating an applicator roller and a pressure roller for respectively applying and pressing the strip on the surface, and which are moved simultaneously crosswise to a deposition path of the strip, so that a contact point between the applicator roller and the surface moves in a radial plane of the support, and a contact point between the pressure roller and the surface moves on a surface generally parallel to the radial plane; the pressure roller being mounted to oscillate about an axis, which is moved simultaneously with the two rollers so as to translate parallel to the radial plane.