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Electrical stress and 10-keV x-ray and 1.8-MeV proton irradiation and annealing responses are evaluated for graphene-based non-volatile memory devices. The memory characteristics of these structures derive primarily from hysteretic charge exchange between the graphene and interface and border traps, similar to the operation of metal-nitride-oxide-semiconductor memory devices. Excellent stability and memory retention are observed for ionizing radiation exposure or constant-voltage stress. Cycling of the memory state leads to a significant reduction in memory window.