One of the key aspects of a detector material for space-borne hard X-ray and gamma-ray telescopes is the rate of prompt and delayed background events generated inside the material by charged and neutral particles striking the detector. These particles are Cosmic Rays, particles trapped in Earth's magnetic field, and secondaries from Cosmic Ray interacting with the atmosphere and the spacecraft. Here, we present a preliminary study of Cadmium Zinc Telluride (CZT) and its behaviour in space environments. We have used the simulation package MGGPOD to estimate the background of the CZT detectors in the proposed Energetic X-ray Imaging Survey Telescope (EXIST ) for possible orbital parameters. The EXIST mission will make use of ∼6 m 2 of >0.5 cm thick CZT detectors to record cosmic X-rays in the energy range from 10 keV to 600 keV. The detectors will be shielded by a fully or partly active shield. For the specific detector and shielding geometry considered here and an orbit with a low (7 • ) inclination, the background rate is dominated by diffuse extragalactic photons below ∼200 keV. Prompt and delayed hadronic backgrounds grow increasingly important above this energy, becoming the main contributors to the total background above ∼1 MeV. A fully active shield performs slightly better than a half active/half passive shield.