                           In this article, analytical approximate solutions of fourth order more critically damped nonlinear differential systems have been studied by applying the modified Krylov-Bogoliubov-Mitropolskii (KBM) method. Further, a fourth order more critically damped nonlinear system has been considered in the event of four equal eigenvalues. In this paper, it has been suggested that the solutions obtained by the modified KBM method conform to those obtained by the numerical method. The method has been described by means of an example.                                                                                                     International Journal of Mathematics and Computation, ISSN 0974-570X (Online), ISSN 0974-5718 (Print), Vol. 28; Issue No. 1; Year 2017, Copyright © 2017 by International Journal of Mathematics and Computation www.ceser.in/ceserp www.ceserp.com/cp-jour