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This paper examines the stability of a multicast tree in the context of a cumulative layered multicast system. In particular it addresses the question, "How does the number of links change us the number of users in a group changes when congestion occurs?" A stability index is defined to evaluate and quantify the stability of such a tree. For obtaining the general expression of the stability index, we develop a simple statistical model and extend it to a more general tree-type: the k-ary balanced tree. We show that the k-values of the k-ary balanced tree have trivial impact on the stability of the tree; however, other parameters in the model, e.g., the dependency-degree factor, the link-marking probability and the tree height, can seriously affect it.