Abstract: Temperament traits in animals may have important fitness consequences, but have received little attention from ecologists or evolutionary biologists. A few studies have linked variation in temperament with fitness, but none has measured selection on temperament traits. We estimated the strength of selection on female boldness and docility on bighorn sheep ewes, Ovis canadensis. The Ram Mountain population experienced little predation pressure during the first 25 years of study, then 2 years (1997 and 1998) of frequent predation by cougars, Puma concolor, during which adult ewe mortality almost tripled over the long-term average, to 27% a year. During years of high predation, we found moderate selection favouring bold ewes, and age-specific selection on docility. Old ewes appeared more vulnerable to predation than young ewes. In contrast, no evidence of selection on temperament traits was observed during 2 years of low predation (1996 and 1999). These results suggest predator-induced selection favouring bold and nondocile ewes. Leadership was highly correlated with age and may increase the risk of predator encounter. Leadership alone, however, could not explain the higher vulnerability of old ewes to predation. Cougar predation on bighorn sheep occurs sporadically and unpredictably, probably because individual cougars often are prey specialists. Cougar predation may have limited microevolutionary effects on temperament in bighorn sheep, because it mostly affects ewes near the end of their reproductive life span and because of potential countervailing selection on boldness and docility. Copyright 2003 Published by Elsevier Science Ltd on behalf of The Association for the Study of Animal Behaviour.