Abstract: In this talk, we will consider a class of Hamiltonian and prove the existence of homoclinic orbits in those systems. This result extends previous existence results by extending the class of Hamiltonian systems. The homoclinic orbits are the limit of infinitely many periodic orbits which are obtained using the mountain pass theorem. Next, we consider a Hamiltonian perturbation of the previous systems and study the convergence of the perturbed solutions to a solution of the original system. The main goal is to obtain homoclinic orbits in the perturbed systems that converge to a homoclinic orbit of the original system. This is an ongoing work with Marek Izydorek and Joanna Janczewska.