In the rotating machinery, such as automobile engines, the driving torque changes periodically and torsional vibrations occur. In this study, the dynamic characteristics of centrifugal pendulum vibration absorbers which are used to suppress torsional vibrations are investigated both theoretically and experimentally. In the theoretical analysis, the nonlinear characteristics are taken into consideration under the assumption that the pendulums vibrate with large amplitude. It is clarified that, although the centrifugal pendulum has remarkable effects on suppressing harmonic vibration, it induces large amplitude harmonic vibrations, the second and third order superharmonic resonances, and unstable vibrations of harmonic type under some condition,. Moreover, this paper proposes various methods to suppress these secondarily induced vibrations, and show that it is possible to suppress torsional vibrations to the substantially zero amplitude-level in the whole rotational speed range.