Abstract: In this paper a method is proposed for the construction of the D-decompositioncurve for an element or a part of a linear control system to determine its stability. Forvarious frequency responses of the element or part, the relative number of roots of thecharacteristic equation with a negative real part can be determined by this method.Methods of using the D-decomposition curves to judge whether all the roots of the charac-teristic equation possess a negative real part are also discussed. It is illustrated in thelast part of the paper that the proposed method can sometimes be employed together withthe describing function method to solve the stability problem of a system with single-valued, nonlinear elements.