The natural γ-activity of shielding and construction materials is very low. For the characterization of the intrinsic activities a very sensitive technique must be applied. In the case of the Ge(Li)γ-spectrometers the photopeak intensities are only significant for extremely low background spectrometers. An essential problem is the correction of the peak rates for attenuation of external background radiation by the sample and for self absorption in the sample. A good measure for the intrinsic activity is the integral background of the γ-spectra between 0.1 and 1 MeV. For investigating high Z materials the X-ray fluorescent peak can be used in a very advantageous manner.