This paper deals with the analysis of Hamiltonian Hopf and saddlecenter bifurcations in ?-DOF systems defined by perturbed oscillators(?:?:?:? resonance). When we normalize the system with respect to the quadratic part of the energy and carry out a reduction with respect to a three-torus group we end up with a ?-DOF system with several parameters on the reduced phase space. Then, we focus on the evolution of relative equilibria. In order to see the interplay between integrals and physical parameters in bifurcations, we consider the classical Stark–Zeeman models.