The　resilience　of　the　drum　of　a　vibration　roller　in　horizontal　and　vertical　directions　reveals　a　hysteresis　pattern　different　from　that　of　the　displacement　during　slant　excitation　compaction.　When　the　soil　compactness　is　high　enough,　the　jump　vibration　and　slipping　of　the　vibration　roller　may　appear.　Considering　the　two　facts　mentioned　above,　kinetic　equations　under　various　compaction　conditions　and　at　different　stages　were　established　in　terms　of　a　model　with　horizontal　symmetric　hysteretic　and　vertical　asymmetric　hysteretic　curves　according　to　soil　property　parameters.　According　to　the　first　order　approximation,　the　hysteretic　resilience　was　linearlized　and　its　equivalent　damping　coefficient　and　equivalent　stiffness　coefficient　were　deduced　by　using　the　harmonic　linearization　method.　By　means　of　numerical　simulation,　the　hysteresis　characteristics　under　three　compaction　conditions　and　correlated　coupled　properties　between　horizontal　and　vertical　directions,　namely,　the　contraction　vibration,　slip-rolling　and　jump　vibration　were　in　turn　analyzed,　and　the　traufer　between　them　was　revealed.　The　adjustment　of　excitation　amplitude　and　excitation　frequency　could　availably　restrain　the　jump　vibration　and　slipping　of　the　drum　to　ensure　the　compaction　quality,　efficiency　and　driving　comfort　in　the　compaction　process.　©　2015,　Chinese　Vibration　Engineering　Society.　All　right　reserved.