A perturbation method is developed for detecting homoclinic connections for the unstable Periodic solution of Duffing's equation with negative linear restoring term. The technique involves a mixture of averaging and singular perturbation methods. Each saddle connection implies a homoclinic point, and the initial bifurcation value of the forcing amplitude is given by the same formula as that obtained by Melnikov's method. The method has also been extended to include an investigation of double loop and transverse saddle connections. Conditions have also been obtained for certain large-amplitude oscillations which are known to occur for this system. The results are illustrated by numerical results for manifolds and saddle connections.