We have been observing the kinetic buildup of electrical conduction current upon x-ray irradiation in ZnSe single crystals. The objective is to understand the behavior of ZnSe crystals under x-ray irradiation, toward their potential use in x-ray detectors that do not require cooling and can operate above room temperature. The paper focuses on the factors that affect the behavior of traps at room temperature. A model is developed to understand the origin of the behavior of the conduction current under x-ray irradiation, taking into account the contributions from three types of traps for electrons (shallow, phosphorescent, and deep) and two luminescence centers (luminescence bands of 630 and 970 nm). Principally, the model is applied to the fitting of the experimental curves. Consequently, the work puts in evidence the role of electron accumulation on traps on the x-ray conduction current buildup on ZnSe crystals. We have obtained experimental dependencies of x-ray conduction current buildup current at 85 K, which indicates the presence of delay in comparison with x-ray luminescence buildup. This paper will demonstrate the effectiveness of our theoretical method in the framework of the multi-center model for wide-gap semiconductors.