Observations of the flight response in mammals are commonly used to test the behavioural response to predation risk. Such a response is likely to be stronger in more sensitive individuals such as females, and females with offspring in particular, as well as during such periods as the birth season. From August 2005 to July 2006 we recorded the flight distances of different mouflon group types in a natural population in Sardinia. The comparison of the flight distances of the groups (n groups=375, n mouflons=1303) provided evidence for the key role of lamb presence. Female groups with lambs fled at greater distances than male groups and female groups without lambs. This difference was linked to the females' priority to secure the survival of their offspring. Indeed, the uniformity of the flight distances of males and non-reproductive females was in contrast to the general expectations regarding ungulate species. In fact, smaller females were expected to be more sensitive to predation risk than larger males. The absence of major differences is probably due to the low sexual dimorphism of mouflon. Flight distances were shorter during the rut than during the lambing season, arguably because during the mating less time and energies were available for anti-predator behaviour. However, during the rut females with lambs still fled at greater distances than females without lambs, arguably because mothers took it as a priority to protect their parental investment rather then to find a potential mate.