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High radiation hardness is the primary requirement for application of lead halide perovskite semiconductors in X-ray detectors for medical diagnostics and solar panels for space missions. Multiple reports show that perovskite absorber films and solar cells indeed could successfully tolerate high electron, proton and neutron fluences as well as gamma rays and x-rays. Among different types of ionizing radiation, gamma rays have very high penetration ability and hence could hardly be mitigated using simple shielding used to suppress the damage from proton and also electron fluences. Thus, the investigation of the radiation hardness of lead halide perovskites with respect to gamma rays is essentially important from fundamental point of view and also in the context of the emerging applications. Herein, we present the results of our systematic study of model lead halide perovskite materials: MAPbI3, FAPbI3, (CsMA)PbI3 and (CsMAFA)PbI3, where MA and FA are methylammonium and formamidinium cations, respectively [3]. We show that all these materials in thin films could tolerate ultra-high doses of gamma rays approaching 10 MGy without significant changes in their absorption spectra. However, among the studied materials FAPbI3 is the only one which does not form metallic lead due to its extreme radiation hardness. Infrared near-field optical microscopy revealed the radiation-induced depletion of organic cations from the grains of MAPbI3 and their accumulation at the grain boundaries, whereas FAPbI3 on the contrary loses FA cations from the grain boundaries. Multication (CsMAFA)PbI3 perovskite undergoes a facile phase segregation to domains enriched with MA and FA cations. This new degradation pathway is quite similar to the gamma-ray-induced halide phase segregation we observed previously for Cs0.15MA0.10FA0.75Pb(Br0.17I0.83)3 material [4-5]. To summarize, our findings suggest that the radiation hardness of the rationally designed perovskite semiconductors could go far beyond the impressive threshold of 10 MGy we set herein for FAPbI3 films, which opens many exciting opportunities for practical implementation of these materials.