Abstract: This paper presents a method that can be applied to analysis of the stability of nonlinear unsteady mechanical systems,based on Chetaev's theory and the theory of the largescale systems: methods of large-scale systems with weighted Vfunction.Moreover,this method is used for the research on the problems of attitude stability of dual-spinning satellite,the large flexible spacecraft and the satellite with cavity containing fluid.It can be seen that this method can be applied effectively to analyzing the stability of the mechanical systems with constraint damping,the gyrosystems and the complex systems of spacecraft.