This study investigates behavioural lateralization in sheep and lambs of different ages. A flock was tested in a task in which the animals were facing an obstacle and should avoid it on either the right or left side to rejoin flock-mates (adult sheep) or their mothers (lambs). A bias for avoiding the obstacle on the right side was observed, with lambs apparently being more lateralized than sheep. This right bias was tentatively associated with the left-hemifield laterality in familiar faces recognition which has been documented in this species. Differences between adult sheep and lambs were likely to be due to differences in social reinstatement motivation elicited by different stimuli (flock-mates or mothers) at different ages. Preferential use of the forelegs to step on a wood-board and direction of jaw movement during rumination was also tested in adult animals. No population bias nor individual-level lateralization was observed for use of the forelegs. At the same time, however, there was a large number of animals showing individual-level lateralization for the direction of jaw movement during rumination even though there was no population bias. These findings highlight that within the same species individual- and population-level lateralization can be observed in different tasks. Moreover, the results fit the general hypothesis that population-level asymmetries are more likely to occur in tasks that require social coordination among behaviourally asymmetric individuals.