We provide a new framework for the analysis of network formation and demonstrate the existence of farsightedly consistent directed networks. Our framework extends the standard notion of a network and also introduces the notion of a supernetwork. A supernetwork is made up of a collection of directed networks (the nodes) and represents (via the arcs connecting the nodes) preferences and rules governing network formation. By extending Chwe’s 1994 result on the nonemptiness of farsightedly consistent sets, we show that for any supernetwork there exists a nonempty subset of farsightedly consistent directed networks.