Abstract: In recent years, the functional form and solution method of the exact stationary solution for multi-degree-of-freedom nonlinear stochastic oscillatory systems under Gaussian white noise excitation were proposed by the present authors using the concepts of integrability and resonance and the property of Poisson bracket in Hamiltonian dynamics. Based on the exact stationary solution, an equivalent nonlinear system method was developed for similar systems. The stochastic averaging method for quasi-Hamiltoni...