The capability of the static VAr compensator (SVC) in damping power system oscillations is investigated on the basis of a Phillips-Heffron model of single-machine infinite-bus power systems. Analysis shows that the ability of the SVC to provide positive damping torque to power systems is influenced not only by the load conditions, as has been found previously, but also by the type (or parameters) of the generator and the strength of the SVC voltage control. It is found that the 'dead point' of the SVC damping control function, which has been reported in two-area power systems, may also exist in a single-machine infinite-bus power system. All the conclusions in the paper have been obtained by theoretical analysis, which ensures their generality and validity in all power systems with the same basic structure, and are confirmed by numerical calculations and nonlinear simulations of an example power system.