The paper presents theoretical basis for identification of nonlinear systems using the method based on Hilbert transform. Discussed method was verified by analyzing the synthesized signals of known parameters. Developed and verified mathematical tools were used for analysis of dynamic responses of the real object: a laboratory (physical) model of the transmission tower. For the considered laboratory model it was possible to simulate damages of individual truss elements and observe changes in system dynamic characteristics. Results of the carried out research proved that the first natural frequency and damping factor change in the observable extent as a result of damage presence.