Centrifugal pendulum vibration absorbers (CPVA) are used in the automobile industry to reduce the vibrations of the transmission system. These passive devices are made of several masses oscillating along a given trajectory relative to the rotor. In this paper, the dynamic stability of a new class of CPVA is investigated. The particularity of this new class is that masses now admit a significant rotation motion relative to the rotor, in addition to the traditional translation motion. The efficiency of such devices is optimal for a perfect synchronous motion of the oscillating masses. However, masses unison can be broken for the benefit of energy localisation on a given absorber, leading to a loss of mitigation performances. To assess the stability of such devices, a dynamical model based on an analytic perturbation method is established. The aim of this model is to predict analytically localisation and jumps of the response. The validity of the model is confirmed through a comparison with both a numerical resolution of the system’s dynamics and an experimental study.