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The need for a network model for the purpose of study of stability of flows is first discussed. A dynamic flow-network model is then presented. It has applications to power networks. A two-matrix transformation method is used to find a suitable Liapunov function. Stability conditions are then obtained when some constraints are imposed on the dynamic components and on the connectivity of the network. The conditions are like a circle criterion, which are on the bounds of the conductances, the memoryless components of the network.