In　this　study,　the　extended　homotopy　analysis　method　(EHAM)　is　applied　to　derive　the　accurate　approximate　analytical　solutions　for　multi-degree-of-freedom　(MDOF)　coupled　oscillators.　The　present　paper　not　only　introduces　the　rationale　for　the　EHAM　for　MDOF　oscillators,　but　also　strengthens　the　availability　of　the　conventional　homotopy　analysis　method　(HAM)　in　solving　complex　MDOF　dynamical　systems.　Employing　the　EHAM　for　the　two-degree-of-freedom　(TDOF)　coupled　van　der　Pol-Duffing　oscillator,　the　explicit　analytical　solutions　of　frequency　omega　and　displacements　x　(1)(t)　and　x　(2)(t)　are　formulated　for　various　initial　conditions　and　physical　parameters.　To　verify　the　accuracy　and　correctness　of　this　approach,　a　number　of　comparisons　are　conducted　between　the　results　of　the　EHAM　and　the　numerical　integration　(i.e.　Runge-Kutta)　method.　It　is　shown　that　the　third-order　analytical　solutions　of　the　EHAM　agree　well　with　the　numerical　integration　solutions,　even　if　the　time　variable　t　progresses　to　a　comparatively　large　domain　in　the　time　history　responses.