Laser scoring of a glass ribbon (13) which moves at a non-constant speed is performed using a tilted track (15) and a carriage (14) which travels down the track. The carriage can include a flying optical head (51) which receives laser light from a flexible laser beam delivery system (61) coupled to a laser (41). Variations in the speed of the ribbon which are less than or equal to ±3% of the ribbon's nominal speed can be accommodated by varying the speed of the carriage and adjusting the output power of the laser (41). Greater speed variations can additionally involve adjusting the tilt angle α the track. Adjustments of the orientation of a first lens unit (53) within the flying optical head (51) can be made to maintain the major axis of the laser beam along the score line as the tilt angle is changed.