Process and device for fast or on-line determination of the components of a two-component or multiple-component system in which the elements which constitute the individual components differ by their atomic number. The following steps are carried out: the surface of the substance is irradiated with polychromatic X-ray or monochromatic gamma radiation, the X-ray radiation exhibiting in the energy range from 1 to 30 keV one or more peaks in the continuum. The spectrum of the radiation backscattered and emitted by the substance is measured in an energy range from 1 to 30 keV with a resolution of at least 250 eV. The spectrum is analysed in that at least the intensities of the elastically backscattered and inelastically backscattered peaks are separately determined and at least some K.sub.a or L.sub.a fluorescence peaks in the energy range from 1 to 30 keV are used in order to compensate for the influence of a fluctuating elemental composition within a component.