We studied sex differences in the nature of aggression and dominance behaviour in two newly formed groups of 1-year-old Icelandic horses. One herd contained nine geldings, the other nine mares. The groups were matched with regard to dominancedetermining traits such as age, weaning age, composition of native herd, social experience, genetic origin, body condition and maternal dominance status. Highranking individuals of both sexes were more aggressive, high-ranking males were older, and high-ranking females had a better body condition. Frequencies of aggressions were similar in both groups. The mares reacted significantly more by showing submission upon an aggression rather than by not responding or by escalating the aggression. For the geldings, this difference was not observed due to a lower tendency to submit. A linear dominance hierarchy was found in both groups. David's scores provided additional information regarding cardinal rank distances and were used to calculate steepness of hierarchies. The female hierarchy was somewhat steeper compared to the male hierarchy, suggesting somewhat lower despotism among males. This was mainly a consequence of the lower unidirectionality in male submission. Male contests occurred predominantly between dyads at top and mid positions, suggesting a low degree of acceptance of the hierarchy.