An X-ray process and device are disclosed for analysing substances and structures. The primary radiation emitted by a radiation source excites a test object to emit secondary radiation, and the secondary radiation is sensed and then evaluated by a receiver. The essential characteristic of the invention is that the passage of the primary or secondary radiation through at least optical elements that consist of a plurality of very thin hollow capillaries, for example made of glass, in which the radiation is paralleled, focused and/or made monochromatic, allows the radiation source or the receiver to be arranged at a distance in space from the test object and low intensity radiation sources to be used. The invention has special application for measuring the thickness of layers, for coupling X-ray fluorescence spectroscopy with microscopy, for designing line optics and for designing a simple but powerful tomograph. A device for continuously measuring in a non-destructive manner the thickness of layers while the layers are produced is illustrated in figure 1.