Centrifugal pendulum vibration absorber (CPVA) systems are used to decrease steady state torsional vibration levels and extend operating ranges for rotating and reciprocating machinery. They are typically sized and designed for a given harmonic using the assumption that a set of identical absorbers move in exact unison. Herein an investigation is carried out to determine the consequences, in terms of system performance, of a recently uncovered dynamic instability of this unison motion. The system considered consists of a rigid rotor and N CPVA's riding on epicycloidal paths tuned to order n, the same as the dominant order of the applied torque. Using two co-ordinate transformations and the method of averaging, the system dynamics can be modelled by a set of 2N first order, internally resonant, autonomous differential equations. A bifurcation analysis of these equations shows that the post-bifurcation dynamics, in which a single absorber moves out of step with its partners, is dynamically stable and leads to the worst-case (that is, the smallest) operating torque range. Furthermore, it is found that the rotor acceleration undergoes a mild saturation, leading to slightly improved performance beyond the instability. Analytical estimates of the torque range and the rotor acceleration are derived based on a truncated version of the equations, and more accurate estimates are obtained from a numerical solution of the non-truncated equations. The results are compared with numerical simulations.