Social psychological investigations of hierarchy formation have been almost entirely confined to the case of task-oriented groups and hence have produced theories that turn on the existence of such a task. But other forms of vertical hierarchy may emerge in non-task groups. One form, orderings of dominance, has been studied among animals using systematic behavioral observations, but almost never among humans, despite many discussions of such structures existing among adolescent males. Using stochastic models, this paper examines change in vertical orderings for data on dominance encounters among same-sex adolescent campers. There seem to be different paths for stabilization of vertical hierarchies for boys and girls, both of which involve the emergence of special roles, the top boy or the bottom girl. Further, stabilization seems to be greatly facilitated (at least for boys) by members adopting Roger Gould's theory of dominance encounters and turning their attention to those close in rank. (Contains 6 figures and 13 footnotes.)