The article is devoted to the theory of Wavelet-transformations with reference to the analysis and synthesis of the dynamic characteristics of the control systems containing an essential nonlinearity of the type of the zone of tolerance, restriction, backlash, etc. of nonlinearity. In the presented work a possibility of application of a device of the theory of Wavelet-transformations for the analysis and synthesis of the dynamic characteristics of the control systems containing essential nonlinearity is considered. A scaling function and wavelet potential function are proposed. The given device has an advantage in comparison with the frequency methods, because it takes into account the processes in the time area. Reactions of the linear systems, including essential nonlinearity, to the influence of a kind of potential function and wavelet are investigated. Errors in the established mode, because of the essential nonlinearities in the tracking system are considered under the influence of the signals representing a Wavelet-number, made of potential functions and wavelet. The condition of stability of the closed-loop system to reaction of the open-loop on the typical influence in the form of a half wave is formulated. The given condition allows us to analyze the stability of the tracking system containing an essential nonlinearity. For this purpose the dependence of the factor of transfer K (j) and the relative delay T3 (j) for the open-loop system, where parameter j characterizes the width of a half wave, is formed. Application of the theory of Wavelet-transformations for the analysis of the nonlinear systems allows us to investigate the complex systems containing the essential nonlinearity as similarly linear systems. The proposed technique of analysis of the nonlinear systems has an advantage in comparison with the frequency methods, because it considers the processes in the time area and allows us to investigate analytically the errors and stability of the tracking systems.