The paper presents a sequential procedure for coordinated stabilization of a multimachine power system with arbitrary complexity of the system model. The most effective machine to be equipped with a power system stabilizer is identified using eigenvalue analysis. The selection is based on the sensitivity of critical eigenvalues to increases in the coefficient of a damping term which is inserted in each equation of motion, in succession. The method is applied to a three-machine system and simulation studies show appreciable improvements in the small disturbance stability of the system.