Generally known conventional X-ray tubes include a window opening which is covered by an X-ray transparent X-ray window which is usually made of beryllium. A significant absorption of X-rays of comparatively long wavelength, for example of the order of magnitude of from 1 nm to 10 nm, occurs in such windows. According to the invention, a bundle of X-ray conducting capillary tubes (46) is connected to the window opening of the X-ray tube, the other end (48) of the bundle being provided with a very thin X-ray window (50) which seals the interior of the capillary tubes (46), being in vacuum contact with the vacuum space of the X-ray tube, from the environment in a vacuumtight manner.