In this paper it is shown that the controller design methodology recently introduced by the authors to stabilize non-globally feedback linearizable triangular systems solves the long-standing problem of transient stabilization of multimachine power systems with non-negligible transfer conductances. The 3n-dimensional (aggregated) model of the n-generator system, with lossy transmission lines, nonlinear loads and excitation control, is considered. A nonlinear dynamic state-feedback control law that ensures, under some conditions on the physical parameters, global asymptotic stability of the operating point is constructed. To the best of the authors' knowledge only existence results—with the restrictive assumption of uniform inertia generators—are available to date for this problem. Simulation results of the New England benchmark system illustrate the performance of the proposed controller.