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Minimizing risk of predation from multiple predators can be difficult, particularly when the risk effects of one predator species may influence vulnerability to a second predator species. We decomposed spatial risk of predation in a 2-predator, 2-prey system into relative risk of encounter and, given an encounter, conditional relative risk of being killed. Then, we generated spatially explicit functions of total risk of predation for each prey species (elk [Cervus elaphus] and mule deer [Odocoileus hemionus]) by combining risks of encounter and kill. For both mule deer and elk, topographic and vegetation type effects, along with resource selection by their primary predator (cougars [Puma concolor] and wolves [Canis lupus], respectively), strongly influenced risk of encounter. Following an encounter, topographic and vegetation type effects altered the risk of predation for both ungulates. For mule deer, risk of direct predation was largely a function of cougar resource selection. However, for elk, risk of direct predation was not only a function of wolf occurrence, but also of habitat attributes that increased elk vulnerability to predation following an encounter. Our analysis of stage-based (i.e., encounter and kill) predation indicates that the risk effect of elk shifting to structurally complex habitat may ameliorate risk of direct predation by wolves but exacerbate risk of direct predation by cougars. Information on spatiotemporal patterns of predation will be become increasingly important as state agencies in the western United States face pressure to integrate predator and prey management.