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We conducted focal observations of territorial guanacos, a highly polygynous and social mammal, to compare time budgets between sexes and test the hypothesis that the differences in reproductive interests are associated with differential group size effects on male and female time allocation patterns. In addition, we used group instantaneous sampling to test the hypothesis that grouping improves detection capacity through increased collective vigilance. We fit GLM to assess how group size and group composition (i.e., presence or absence of calves) affected individual time allocation of males and females, and collective vigilance. As expected from differences in reproductive interests, males in family groups devoted more time to scan the surroundings and less to feeding activities compared to females. Both sexes benefited from grouping by reducing the time invested in vigilance and increased foraging effort, according to predation risk theory, but the factors affecting time allocation differed between males and females. Group size effects were significant when females were at less than five body-lengths from their nearest neighbour, suggesting that grouping benefits arise when females are close to each other. Female time budgets were also affected by season, topography and vegetation structure. In contrast to our expectation, males reduced the time invested in vigilance as the number of females in the group increased, supporting the predation risk theory rather the intrasexual competition hypothesis. The presence of calves was associated with an increase in male individual vigilance; and vegetation type also affected the intensity of the group size effect over male time allocation. In closed habitats, collective vigilance increased with the number of adults but decreased with the number of calves present. Although male and female guanacos differed in their time allocation patterns, our results support the hypothesis that both sexes perceive significant antipredator benefits of group living. [ABSTRACT FROM AUTHOR]