The effects of gamma-irradiation at 77 K on two crystalline forms of water, namely, cubic and hexagonal ice, and on two amorphous forms of water, made by hyperquenching of liquid water or deposition of water vapors, have been studied by electron spin resonance (ESR) spectroscopy. Mainly OH radicals are formed from cubic ice directly made from liquid water. In contrast, comparable amounts of OH and HO2 radicals are formed on irradiation of cubic ice made by heating glassy water, and their relative yields depend strongly on the irradiation dose. Comparable yields of OH and HO2 radicals were observed on gamma-irradiation of the two amorphous solids, and their ratio did not depend on irradiation dose. The formation of HO2 radicals is attributed to the presence of shallow proton traps, or Bjerrum-like L-defects, in the two amorphous solids and in disordered regions of cubic ice.