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Social stability in semiferal ponies: networks show interannual stability alongside seasonal flexibilityLong-term relationships that underlie many stable mammalian groups often occur between philopatric kin. Although stable groups of nonrelatives appear to be less common, there is increasing evidence that social bonds between nonkin may confer sufficient intrinsic fitness benefits for these groups to persist. Here we evaluate whether social stability occurs in a bisexually dispersing species where social bonds have been shown to have reproductive benefits: the feral horse, Equus caballus. First, we quantified female social stability by applying a three-level framework to a 3-year data set of associations in semiferal ponies; this tested for stability at the individual, dyadic and subpopulation levels. Despite the relative weakness of these female bonds, we found significant social stability across all levels, as shown by stable association preferences, social networks and individual network positions. Second, we investigated how seasonality impacts on social bond strength and grouping patterns. We found seasonal fluctuations in female gregariousness, with a peak during the mating season. We therefore propose that significant social stability in female horses is coupled with a degree of flexibility that allows for effects of ecological fluctuations. Although social network analysis is widely used in behavioural ecological research, this is one of only a handful of studies to assess the temporal dynamics of networks over a significant timescale. Temporal stability in female relationships suggests that equid social structures are multifaceted: although bonds between stallions and mares are clearly strong, long-term relationships between mares underpin the social network structure. We suggest this framework could be used to assess social stability in other group-living species in order to improve our understanding of the nature of social bonds.