The activity budget hypothesis has been proposed to explain the social segregation commonly observed in ungulate populations. This hypothesis suggests that differences in body size--i.e. between dimorphic males and females--may account for differences in activity budget. In particular, if females spend more time grazing and less time resting than males, activity synchrony would be reduced. Increased costs of maintaining synchrony despite differences in activity budget would facilitate group fragmentation and instability of mixed-sex groups. In this paper two prerequisites of the activity budget hypothesis were tested: (1) that males should spend less time feeding and more time resting than females in single-sex groups and (2) that lower activity synchrony should be observed in mixed-sex compared to single-sex groups. The activity budget and synchrony in mixed and single-sex groups of merino sheep (Ovis aries) of different sizes (2, 4, 6, 8 individuals) were measured in three contiguous 491-m2 arenas located in a natural pasture. Three same-size groups, one of each category, were observed simultaneously. We found no sexual differences in the time spent inactive and active (i.e. grazing, standing, moving, interacting). Males spent significantly more time grazing and less time standing than females. These differences disappeared when yearling males were omitted from the group. Males and females had similar bite and step rates. Sheep of both sexes spent less time resting and more time grazing and moving and had lower bite rates when in mixed-sex groups than when in single-sex groups. The synchrony among visually isolated groups was near zero, indicating that they changed activities independently. On the contrary, within-group synchrony was high; however it was higher in single-sex groups, in particular for males, than in mixed-sex groups. Our results suggest that differences in activity budget and synchrony alone are insufficient to explain social segregation.