A simplified analysis of the effect of a static reactive-power (VAr) compensator (SVC) on the stability of a two-machine system is presented. This analysis shows that the SVC's damping effectiveness is greatly affected by a self-feedback term, whereby a change in SVC suceptance changes the measurement signal which is used to control the SVC. Recognition of this term explains why some control signals are superior to others, and why an SVC might offer limited damping improvement, even with a high-gain damping control. Results of a transient simulation are presented which show that, with a suitable control and a suitable location, an SVC can offer a marked improvement to the damping of rotor-angle oscillations in a power system. The high effectiveness of the SVC in rapidly changing the power flow makes the correct control decision essential during the fault period; guidelines for the control strategy during the fault are presented.