In 2011, a network of five thallium-doped sodium iodide (Nal(Tl)) detectors was installed on Aragats Space Environmental Center (ASEC) and was included into ASEC detectors system. Along with monitoring of different species of secondary cosmic rays, ASEC detectors register several thunderstorm ground enhancements (TGEs). NaI(Tl) detector integration in the ASEC detector system is of great importance for the study of thunderstorm phenomena for the reason that NaI(Tl) detectors have a higher efficiency of gamma rays detection compared with plastic ones. In this article, the design and characteristics of NaI(Tl) detectors are described. Simulations of detector response are performed. Comparison of simulation results with experimental data showed good agreement between simulations and experimentally observed distributions for analog-to-digital converter (ADC) channels (codes) of NaI(Tl) detectors at two depths of the atmosphere, thus, indicating the correctness of the detector׳s response determination. A procedure for reconstruction of gamma energy spectrum was developed and approximation of the energy spectrum of recorded TGE event was carried out by a power function under the assumption that the recorded fluxes consist mainly of gamma quanta.