Abstract: In this paper, according to the form of the asymptotic solution of papers [1, 2], the asymptotic method is extended to the following a class of more general strong nonlinear vibration systems

where g and f are the nonlinear analytical-functions of x and x, and ε>0 is a small parameter. We assume that the derivative system corresponding to ε=0 has periodic solution. The recurrence equations of the asymptotic solution for the system(0.1)are deduced in this paper, and they are applied to practical examples.