In recent years, room temperature semiconductor detectors like CdTe and CdZnTe have been proposed for several scientific, industrial and medical applications. In some cases, these applications require the capability to operate for a long time in intense, sometimes mixed, radiation fields while retaining full spectroscopic performances. In spite of its importance, a detailed characterization of the effects of the radiation damage has not been competed yet for these materials. However, preliminary results carried out by irradiating CdTe detectors with 60Co gamma rays demonstrated that the fatal photon dose is on the order of some tens of thousands Gy, while the detectors are rather insensitive to doses up to few thousands Gy. A wider activity is now being performed by the authors studying both the CdTe and the CdZnTe when involving several types of irradiating sources and different techniques to quantify the induced damaging. This includes the detailed quantitative analysis of retained spectroscopic performances at low and medium energies, the measurement of the dark current and the characterization of the defects and modifications induced in the structure of the crystal by the irradiation process.