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[1] Solar hard X-ray flares can expose astronauts on lunar and deep space extravehicular activities (EVAs) to dangerous acute biological doses. We combine calculations of radiative transfer through shielding materials with subsequent transfer through tissue to show that hazardous doses, taken as ≥0.1 Gy, should occur with a probability of about 10% per 100 hours of accumulated EVA inside the current spacesuit. The rapid onset and short duration of X-ray flares and the lack of viable precursor events require strategies for quick retreat, in contrast to solar proton events, which usually take hours to deliver significant fluence and can often be anticipated by flares or other light speed precursors. Our results contrast with the view that only particle radiation poses dangers for human space exploration. Heavy-element shields provide the most efficient protection from X-ray flares, since X rays produce no significant secondary radiation. We calculate doses due to X-ray flares behind aluminum shields and estimate the required shield masses to accompany EVA rovers.