This paper introduces the problem of n mobile agents that repeatedly visit all n nodes of a given network, subject to the constraint that no two agents can simultaneously occupy a node. It is shown for a tree network and a synchronous model that this problem has O(Δn) upper and lower time bounds where Δ is the maximum degree of any vertex in the communication network. The synchronous algorithm is selfstabilizing and can also be used for an asynchronous system. A second algorithm is presented and analyzed to show O(n) round complexity for the case of a line of n asynchronous processes.