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In this paper, the problem of electric circuit identification has been studied. Topological singularities in a circuit structure are found to be the origins of ill-conditionality of a circuit model. It has been shown that it is useless to solve an ill-conditioned identification problem due to a considerable distortion of experimental data by measurement errors. No information on the exact solution can be extracted from these data except for linear relations between elements of the solution. A new circuit identification algorithm, named the repeat measurements principle, was developed based on the linear relations mentioned above. The algorithm showed a high efficiency for any degree of model ill-conditionality and allowed us to determine model parameters accurate to the measurement precision as applied to any type of reciprocal and non-reciprocal linear circuits.