Abstract: A dynamic model of an impact-progressive system is established. The regularity and transition of two types of periodic-impact motions are studied, and the condition for judging the progressive motion of a system is put forward. The dynamic behaviour and the influence of system parameters on progression rate are investigated by numerical simulations. The impact mapping of a vibro-impact system with repeated inelastic impacts is of piecewise property due to synchronous and non-synchronous motions of impact components immediately after the impact, and singularities caused by the grazing contact motions of impact components. The piecewise property and grazing singularity of impact mapping of such systems lead to non-standard bifurcations of periodic-impact motions. The results indicate that the n ? p motion transits to long-periodic multi-impact motion or chaotic motion immediately via grazing bifurcation. The maximum impact velocity of the mass M1 and the largest progression of the system are found to occur during period-1 single-impact motion with a peak impact velocity.