To improve a known method for making a quartz glass tube as a semifinished product for the manufacture of optical fibers, the tube comprising an inner fluorine-doped quartz glass layer and an outer quartz glass layer, so as to achieve inexpensive manufacture and improved dimensional stability of the quartz glass tube, it is suggested according to the invention that the quartz glass of the inner layer should be produced in a first plasma deposition process with formation of an inner layer having a wall thickness of at least 1.5 mm, with a fluorine content of at least 1.5% by wt. being set in the quartz glass, and that the quartz glass of the outer layer should be produced in a second plasma deposition process and deposited directly or indirectly on the inner layer with formation of a composite tube, and that the composite tube should be elongated into the quartz glass tube.