This paper presents a separation result for some global stabilization via output feedback of a class of quadratic-like nonlinear systems, under the form of some “stabilizability by state feedback” on the one hand, and “unboundedness observability” on the other hand. They allow to design, for any domain of output initial condition, a dynamic output feedback controller achieving global stability. As an example, these conditions are shown to be satisfied by so-called “Euler-Lagrange” systems, for which a tracking output feedback control law is thus proposed.