In this paper, two methods, namely Homotopy Perturbation Method(HPM) and Homotopy Analysis Method (HAM) are applied to obtain approximatesolutions of the nonlinear coupled Hirota system (CHS). We see that these twomethods are efficient and effectives for solving nonlinear CHS and the obtainedresults of the two methods coincide with each other. In our work, Maple 13 hasbeen used for computations.