The paper deals with the harmonic resonance problem. At the beginning, disadvantages of the only viable method for resonant investigations, i. e. the method based on frequency scan analysis of the node impedances, are enumerated. Then, the theoretical background for the calculations of resonant frequencies is presented. In the paper one utilizes description of the system with use of state equations. After the conditions of occurrence of resonance are described, the manner of calculation resonant frequencies is discussed. The proposed approach is illustrated by two examples. In the first example a simple RLC circuit is considered, in the second one for the IEEE 14-bus test system the resonant investigations are made. At the end, the features of the described approach are analysed.