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This paper presents a topological formulation of Liapunov stability conditions for linear and nonlinear time-varying RLC networks. In other words, Liapunov stability theorem for linear time-varying RLC networks obtained by Kuh is formulated in terms of the tree or chord-set products of the subnetworks derived from the state-space representation of the networks and the same approach is extended to the local stability of nonlinear time-varying RLC networks. The new formulation provides stability information or stability criteria in terms of network elements for linear and nonlinear time-varying RLC networks by inspection of the topology and network elements. The above formulation is illustrated in detail by the use of examples.