This paper investigates the problem of designing distributed control laws making a group of dynamic unicycles converge to a common circle of prespecified radius, whose center is stationary but dependent on the initial conditions, and travel around the circle in a desired direction. The vehicles are required to converge to a formation on the circle, expressed by desired separations and ordering of the unicycles. The information exchange between unicycles is modelled by a directed graph which is assumed to have a spanning tree. A hierarchical approach is proposed which simplifies the control design by decoupling the problem of making the unicycles converge to a common circle from the problem of stabilizing the formation.