A method for forming a hollow cylinder, in a single step, into a quartz glass tube with a large outer diameter and high dimensional stability is provided. To produce the tube, the cylinder, while rotating, is softened in portions in a heating zone which is moved at a relative feed rate Va and the softened portion is radially expanded by a centrifugal force and/or internal overpressure applied in the hollow cylinder bore so as to form a deformation zone. The radial expansion of the softened portion is carried out at a location-dependent radial expansion rate Vr, the profile of which along the deformation zone has a maximum value Vr,max which is smaller than 20 cm/min. The temperature in a rear heating portion of the heating zone, assigned to the end of the deformation zone, is lower than in a front heating portion assigned to the beginning of the deformation zone.