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The paper treats an inverse problem posed in the time domain for a circuit described by a stiff system of ordinary differential equations (ODEs). Identification of model parameters (circuit elements) is performed by processing transient characteristics measured in the circuit. An illustrative example discussed throughout the paper shows that reducing the identification problem to curve fitting, which is the most general way, may be hardly used for a stiff model due to a ravine shape of the objective functional. Moreover, a necessity of solving the stiff ODE system to get a functional value makes the inverse problem be practically unsolvable. It has been shown that the initial inverse problem may be simplified significantly by taking into account linear relations which are observed between the experimental characteristics measured for a stiff system. The relation coefficients are discussed in the paper with regard to the accuracy of the approximation. Finally the initial identification problem has been reduced to a nonlinear system of algebraic equations which may be easily solved considering different sensitivity of the relation coefficients to the model parameters. The final solution is presented for different levels of "measurement" error involved in the simulation.