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The irradiation and annealing responses of 4H-SiC MOS devices with nitrided oxides are investigated at varying biases. Radiation-induced hole trapping dominates the radiation response of these devices. Switching the bias between irradiation and annealing can lead to significant enhancement of the degradation in some cases. Positive irradiation bias followed by negative annealing bias is found to be the worst-case for the combined degradation. After irradiation, significant reversibility of charge trapping is observed in switched-bias annealing of n-substrate capacitors, while enhanced charge trapping is found in p-substrate capacitors. These results show the potential importance of evaluating the combined radiation and reliability responses of SiC MOS devices for long-term use in high total-ionizing-dose space applications.