Abstract: From the solution of the Lyapunov equation, the stationary random vibration response covariance of a structure can be directly obtained. The nonlinear system is linearized by the equivalent linearization method, and the Lyapunov equation is solved by iterations and the stationary equivalent linear parameter of the nonlinear system is obtained. This is a characterization method for the nonlinear vibration system of multiple degrees of freedom (DOFs). The proposed method provides a theoretical basis to choose the model of the nonlinear dynamic system. A simulation is carried out to analyze an examples of the nonlinear system, and the results show that this method is valid.