Abstract
In this article, an approximate technique has been presented for obtaining the analytical approximate solutions of second order strongly nonlinear differential systems with small damping and slowly varying coefficients based on the He's homotopy perturbation and the extended form of the Krylov-Bogoliubov-Mitropolskii methods. An example is given to illustrate the efficiency and implementation of the presented method The first order analytical approximate solutions obtained by the presented method show a good agreement with the corresponding numerical solutions for the several damping effects.