Dominance hierarchies in groups of social animals can be based either on asymmetries that are important for agonistic interactions (such as body mass) or on more ‘conventional’ cues (such as age), which are respected despite having little relationship to the animal’s fighting abilities. We investigated how social dominance is influenced by age and body mass in a herd of 29–39 beef cows over a 10-year period, focusing on all levels of the dominance hierarchy (individual, dyadic and group). The results demonstrate that age prevails over body mass in the structuring of the dominance network in beef cattle. At the individual level, path analysis confirmed that the dominance index of a cow was more strongly associated with her age than with her body mass. At the dyadic level, age superiority had a stronger influence on the direction of social dominance in pairs than body mass superiority. Older cows were dominant in 73,6% of those dyads studied, even when the younger cow was heavier. At the group level, the strong influence of age on dominance produced a hierarchy that was very stable and strongly transitive. Our findings show that beef cows, for the most part, do not use their physical strength to attain dominance over older, but lighter, herdmates. This results in a stable age-based hierarchy, which might serve a universally shared function that promotes the smooth functioning of the herd and/or the expression of experience by older cows. Among the theoretical models of conflict resolution, the system most closely resembles the partial bourgeois evolutionarily stable strategy.