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A theory for the study of the analog circuit fault diagnosis problem is developed. Sufficient conditions are presented such that the value of each of the network elements is uniquely determinable from the network's behavior as seen from its external terminals. It is shown how one can determine-considering only the circuit's topology-whether or not it is possible to compute the element values of a resistive network from the test-terminal measurements, before going through the process of actually attempting to solve for element values. The implications of the results are discussed when applied to networks containing solid-state devices such as diodes and transistors. Finally, an algorithm for the actual computation of the element values is proposed and its global convergence is proved. Furthermore, several examples are included to illustrate the applications of the theory developed in this paper.