A method and apparatus are provided for producing a tube of glass by zonewise heating and softening of a hollow cylinder by a movable heating zone while rotating about its rotation axis. The glass tube is continuously formed by radial expansion of the softened region under action of centrifugal force and/or internal overpressure applied in the hollow-cylinder bore. The method and apparatus make it possible to deform the hollow cylinder in a single or a small number of forming steps into a glass tube having a larger outer diameter and high dimensional accuracy by determining a circumferential position at which the wall thickness is comparatively small, and during heating and softening of the rotating hollow cylinder a coolant is dispensed from a coolant source onto the deformation zone only when or predominantly when the circumferential position having the comparatively small wall thickness passes the coolant source.