We　investigate　dynamic　characteristics　of　vibratory　compaction　system　with　asymmetrical　hysteresis.　An　asymmetrical　model　derived　from　Bouc-Wen　differential　equation　is　employed　to　describe　hysteretic　behavior　of　vibration　engineering.　A　practical　polynomial　expression　for　hysteretic　restoring　force　is　deduced　to　be　substituted　into　standard　equation　of　the　system,　assuming　that　the　non-linearity　of　the　restoring　force　is　weak.　An　asymptotic　method,　which　combines　Krylov-Bogolyubov-Mitropolsky　(KBM)　method　with　harmonic　balance　(HB)　method,　is　applied　to　analyze　steady-state　responses　of　the　asymmetrical　hysteretic　system　subjected　to　harmonic　excitation.　Dynamic　responses,　such　as　the　restoring　force　time　histories　and　frequency　responses　of　the　system　for　the　first　order　approximate,　are　obtained.　Furthermore,　numerical　solution　obtained　using　Runge-Kutta　method　as　well　as　results　of　experiments　(asphalt　compaction　on　the　Beijing-Fuzhou　highway)　are　compared　with　the　asymptotic　solution.　These　results　investigated　that　asymmetrical　hysteretic　model　and　the　methods　applied　in　this　paper　are　quite　appropriate　for　engineering　applications.