Innumerable　engineering　problems　can　be　described　by　multi-degree-of-　freedom　(MDOF)　nonlinear　dynamical　systems.　The　theoretical　modelling　of　such　systems　is　often　governed　by　a　set　of　coupled　second-order　differential　equations.　Albeit　that　it　is　extremely　difficult　to　find　their　exact　solutions,　the　research　efforts　are　mainly　concentrated　on　the　approximate　analytical　solutions.　The　homotopy　analysis　method　(HAM)　is　a　useful　analytic　technique　for　solving　nonlinear　dynamical　systems　and　the　method　is　independent　on　the　presence　of　small　parameters　in　the　governing　equations.　More　importantly,　unlike　classical　perturbation　technique,　it　provides　a　simple　way　to　ensure　the　convergence　of　solution　series　by　means　of　an　auxiliary　parameter　h.　In　this　paper,　the　HAM　is　presented　to　establish　the　analytical　approximate　periodic　solutions　for　two-degree-of-freedom　coupled　van　der　Pol　oscillators.　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　higher-order　analytical　solutions　of　the　HAM　agree　well　with　the　numerical　integration　solutions,　even　if　time　t　progresses　to　a　certain　large　domain　in　the　time　history　responses.　Copyright　©　2009　by　ASME.