Simultaneous overlay networks compete for physical network resources and disrupt each other. If they could establish cooperative relationships, the collective performance can be improved and they can coexist peacefully and comfortably. Taking inspiration from biology, in this paper we present a model of symbiotic overlay networks. Coexisting overlay networks dynamically evolve, interact with each other, and change their internal structures. Overlay networks in a symbiotic condition, i.e., mutualism, eventually establish the strong relationship and finally fuse into one. We first analyze characteristics of an overlay network which evolves based on three different models, i.e., the preferential attachment, random, and combination of them, by using mathematical analysis and simulation experiments. Next, we evaluate the effect of interconnecting two overlay networks from the viewpoint of the cost and the benefit.