A method of continuously processing glass ribbon having a thickness ≤0.3 mm. The method includes providing a glass processing apparatus having a first processing zone, a second processing zone and a third processing zone. The glass ribbon is continuously fed from the first processing zone, through the second processing zone to the third processing zone. The feed rate of the glass ribbon is controlled through each processing zone using a global control device. A first buffer zone is provided between the first processing zone and the second processing zone in which the glass substrate is supported in a first catenary between two, spaced-apart, payoff positions. A second buffer zone is provided between the second processing zone and the third processing zone in which the glass substrate is supported in a second catenary between two, spaced-apart, payoff positions.