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Nonlinear resistive networks, which can be characterized by the equation , where is a continuous piecewise linear mapping of into itself, are discussed. is a point in and represents a set of chosen network variables and is an arbitrary point in and represents the input to the network. New theorems on the existence of solutions together with a convergent method for obtaining at least one of the solutions are given. Also dealt with is an efficient computational algorithm which is especially suited for analysis of large piecewise-linear networks. The effectiveness of the method in terms of the amount of computation and data handling and storage is demonstrated.