Abstract: An inverse relationship between individual vigilance level and group size is widely reported in many behavioral studies on animals across several taxa. It is generally held that such a relationship is due to a reduced probability of an individual being killed in larger groups. in the present investigation, I studied the vigilance behavior of the endangered Tibetan argali Ovis ammon hodgsoni in relation to group size and escape terrain. I hypothesized that an individual argali has a higher vigilance level in smaller groups and in habitats closer to cliffs than individuals living in larger groups and open areas (escape terrain). The results show that the vigilance of argali decreased with increasing group size, but there was no effect of escape terrain on its vigilance behavior. There were significant differences between age-sex groups: male, female and yearling in their time budgets. Females, compared to males and yearlings, spent more time being vigilant. They also foraged more and moved less than males. It is suggested that vigilance is an important anti-predator behavior amongst argali sheep.