This work studies the conductivity and luminescence of ZnSe single crystals under X-ray irradiation. The experimentally derived lux-ampere characteristics of the X-ray conductivity for ZnSe crystals have a sublinear behavior within the temperature range from 8 to 420 K. The theoretical analysis of the conductivity kinetics at X-ray excitation showed that the value of maximum accumulated lightsum at deep traps does not depend on radiation intensity. However, regarding shallow and phosphorescent traps, the strength of accumulated lightsum depends on the intensity of exciting irradiation. Specifically, these shallow traps and phosphorescent traps cause the sublinear behavior of lux-ampere characteristics in the semiconductor material.