In　this　paper,　the　homotopy　analysis　method　(HAM)　is　presented　to　establish　the　accurate　approximate　analytical　solutions　for　multi-degree-of-freedom　(MDOF)　nonlinear　coupled　oscillators.　The　periodic　solutions　for　the　three-degree-of-freedom　(3DOF)　coupled　van　der　Pol-Duffing　oscillators　are　applied　to　illustrate　the　validity　and　great　potential　of　this　method.　For　given　physical　parameters　of　nonlinear　systems　and　with　different　initial　conditions,　the　frequency　omega,　displacements　x(1)　(t),　x(2)(t)　and　x(3)(t)　can　be　explicitly　obtained.　In　addition,　comparisons　are　conducted　between　the　results　obtained　by　the　HAM　and　the　numerical　integration　(i.e.　Runge-Kutta)　method.　It　is　shown　that　the　analytical　solutions　of　the　HAM　are　in　excellent　agreement　with　respect　to　the　numerical　integration　solutions,　even　if　time　t　progresses　to　a　certain　large　domain　in　the　time　history　responses.　Finally,　the　homotopy　Pade　technique　is　used　to　accelerate　the　convergence　of　the　solutions.　(C)　2009　Elsevier　B.V.　All　rights　reserved.