Methods and apparatus for guiding flexible glass ribbons (13) without mechanically contacting the central portion (4) of the ribbon are provided in which two curved sections are formed in the ribbon which stiffen the ribbon so that lateral forces can be applied to the ribbon without causing it to buckle. The curvatures of the curved sections are along the direction of motion (15) of the ribbon and can be produced using curved air-bars (12,14) and/or pairs of cylindrical rollers (5a,5b,16a,16b). The lateral forces can be applied by pairs of guide rollers (7a,7b,9a,9b) which can be mounted on spring-loaded pivot arms (6,19,29) and can have a complaint outer coating or sleeve (35). The guiding system can be used in the winding of the glass ribbon onto a cylindrical core (11).