The relevance of the study. At the present stage of development of CIS countries network the first-priority problem is increase of operation reliability of transformers, the main part of which has been out of date long ago. The main aim of the study is to state the main reasons of discrepancy between the research methods and the essence of the problem, which is under study, and to establish possible areas of improvement. The methods used in the study: frequency methods of natural experiment and electrical circuit analysis. The results. The reason of discrepancy between the used research methods and the essence of the problem is the assumption of possibility to consider electrical and magnetic fields of the single electromagnetic field separately. The combined consideration of the single electromagnetic field shows the distributed parameter line (which is represented by the windings and their parts) is heterogeneous. Conclusions. Adequate representation of real physical processes in transformer windings by mathematical models is impossible without modeling both intrinsic leakage resistance of windings and their parts and mutual induction resistance between these parts, taking into consideration the failure of reciprocity principle of mutual induction in real transformers. The authors have developed the method of implementing the functions of complex impedance frequency characteristic. The method proposes to move from implementation of function of two independent variables Z(p) = Z(jw) = R(w) + jX(w) to implementation of two independent functions of one variable ZR(w) = R(w) и ZX(w) = X(w). The method also eliminates the need for Z(p) approximation as a ratio of two polynomes, which do not have common roots. The correct usage of the methods of the calculation theory for electric circuit with lumped parameters allows analyzing the parameters of electromagnetic processes in specific points of the object with distributed parameters involving the interaction between its longitudinal elements. The existing world technical publications about electromagnetic processes in large transformers at internal resonances, cannot be called trustworthy, if the results described were obtained using the calculation theory of electric circuit with lumped parameters without adding the necessary corrections.