An experimental procedure for determination of the reduced thicknesses of thin films of contamination layers is described. It becomes possible to determine the energy dependence of the attenuation length in contamination layers from the angular distribution of photoelectron and Auger signals from the substrate at different kinetic energies. Within a restricted interval of electron energies, the attenuation length is proportional to E(kin)m. The evaluation of our experimental results gave a value of m = 0.64 in the energy range 0.4 keV less-than-or-equal-to E(kin) less-than-or-equal-to 1.4 keV. From considerations of the influences of surface roughness and the finite solid angle of acceptance on measured m values it must be expected that the true value of m is larger than 0.64. Since these two influences on measured characteristic photoelectron signals will occur in practice too, we propose an effective value m = 0.64 for correction of the energy dependent attenuation in contaminations.