For the first time, the change in the real and imaginary parts of Cd1–xZnxTe crystals complex dielectric permittivity when exposed to ionizing radiation with a small exposure dose rate (about hundreds of μR/h) has been studied. Significant changes in the values of both parts of complex dielectric permittivity have been revealed. Regularities of specified changes have been established and explained taking into account a different radiation effect on free and bound charges. The basis of effect is the changes in the charge carrier localized states of point defect associates. Their appearance is due to a high concentration and a variety of intrinsic structural defects in the studied crystals as a consequence of the deviation of the crystal composition from the stoichiometric one.