Existing theory and practice use the classical law of exponential attenuation of X-ray radiation (XRD) during its passage in matter (Bouguer's law). However, as a result of exploratory experimental studies it was found that in materials containing small particles of metallic ultradispersed powders (UDP) of certain concentrations, there are significant deviations from the Bouguer law (up to 40-60% of the classical RI absorption curve). On the discovered phenomenon of anomalous RI absorption by materials containing UDP, in April 1994, a diploma on the discovery was received.