Indirect interactions among species can strongly influence population dynamics and community structure but are often overlooked in management of large mammals. We estimated survival of Dall's sheep (Ovis dalli) in the central Alaska Range, USA, during years of differing snowshoe hare (Lepus americanus) abundance to test whether indirect interactions with a cyclic hare population affect Dall's sheep either negatively, by subsidizing predators (apparent competition), or positively, by diverting predation (apparent commensalism). Annual survival of adult female sheep was consistently high (0.85 for all yr and age classes combined). In contrast, annual estimates of lamb survival ranged from 0.15 to 0.63. The main predators of lambs were coyotes (Canis latrans) and golden eagles (Aquila chrysaetos), which rely on hares as their primary food and prey on lambs secondarily. Coyotes and eagles killed 78% of 65 radiocollared lambs for which cause of death was known. Lamb survival was negatively related to hare abundance during the previous year, and lamb survival rates more than doubled when hare abundance declined, supporting the hypothesis of predator-mediated apparent competition between hares and sheep. However, stage-specific predation and delays in predator responses to changes in hare numbers led to a positive relationship between abundance of adult Dall's sheep and hares. Lacking reliable estimates of survival, a manager might erroneously conclude that hares benefit sheep. Thus, support for different indirect effects can be obtained from different types of data, which demonstrates the need to determine the mechanisms that create indirect interactions. Long-term survey data suggest that predation by coyotes is limiting this sheep population below levels typical when coyotes were rare or absent. Understanding the nature of indirect interactions is necessary to effectively manage complex predator–prey communities.