The asymptotic behavior of autonomous oscillating system describing by differential equation of fourth order with small non-linear external perturbations of "white noise", non-centered and centered "Poisson noise" types is studied. Every term of external perturbations has own order of small parameter ". If small parameter is equal to zero, then general solution of obtained non-stochastic fourth order differential equation has an oscillating part. We consider given differential equation with external stochastic perturbations as the system of stochastic differential equations and study the limit behavior of its solution at the time moment t[epsilon]k, as [epsilon] ["з… випливає" або "якщо…, то…"] 0. The system of averaging stochastic differential equations is derived and its dependence on the order of small parameter in every term of external perturbations is studied. The case of multiple real root and two conjugate pure imaginary roots of characteristic equation is considered.