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In this paper a diagnostic method for analog electronic circuits is presented. The approach is based on determination of the variations of circuit functions with use of higher order sensitivity coefficients. Knowing values of sensitivity coefficients one can formulate multivariate polynomial equations. The solution of test equations with respect to element's deviations results in fault identification. This task can be realized by using Grobner bases to transform a nonlinear equation into triangular form. It is solved by successive computation of the univariate polynomial equation and back substitution. Solution of the polynomial equation is treated as the eigenvalue problem of companion matrix by QR algorithm. Numerical results are presented to clarify method and prove its efficiency.