In the paper some considerations are presented in order to capture the potentiality of Flexible Alternating Current Transmission Systems (FACTS) devices in improving the dynamic performances of power systems. More specifically, these devices can enlarge the attraction region of power systems equilibrium points, allowing to increase the stability margin following large perturbations. In the paper, the boundary of the attraction region of the post-fault stable equilibrium point for a simple power system in presence of FACTS devices, is estimated by means of a quadratic function, which provides a good approximation and an analytical expression which could result very useful for sensitivity analysis. Supplementary controllers to FACTS devices, are also proper means for obtaining an increased damping of interarea oscillations which are inherent in large power systems. A linearized modeling is employed for identifying the countermeasures to face with this complex phenomenon, also taking into account the presence of delay in transmitting remote control signals. In the last part of the paper some numerical applications with respect to test system are reported showing the usefulness of the considerations presented.