In this paper we study the non-linear dynamic of centrifugal pendulum vibration absorbers (CPVA), and we pay a special a ention to localized state solutions. e prediction of such states of vibration, and their stability, is of particular importance because they can lead to inefficient behavior for the CPVA and/or unforeseen stress levels. Using an approximated equation for the pendulums dynamics, we derive initial conditions to put the system in localized states. Following an analytic study of the non-linear normal mode of the system, the resolution of the approximated equation is carried out in the frequency domain using the Harmonic Balance Method and the Asymptotic Numeric Method. For sufficiently low inertia ratio, we show that the system can possess stable localized states.