Known synthetic quartz glass tubes for the production of a preform have an inner bore with a surface layer produced without using tools in the molten state and an inner zone. The aim of the invention is to provide a tube which does not release any OH groups to the surroundings. For this purpose, the surface layer (30) has a thickness of 10 μm and an average OH content of not more than 5 ppm by weight and an average surface roughness Ra of not more than 0.1 μm. The inner zone (34) that starts on the surface layer (30) and terminates 10 μm before the outer wall has an average OH content of not more than 0.2 ppm by weight. A simple and inexpensive method for producing a quartz tube of the above type is to continuously draw a tube strand from a softened quartz glass mass in a vertical drawing process. A scavenging gas is circulated through the inner bore of the tube, said gas having a water content of less than 100 ppb per weight. The front end of the tube strand (19) is closed by a flow obstacle (26) that is permeable the scavenging gas and that reduces the amount of scavenging gas (23) flowing through.