Relaxation　oscillations　are　typical　fast-slow　behaviors　in　the　excited　Duffing　system.　The　present　paper　focuses　on　the　effects　of　amplitude-modulated　excitation　on　relaxation　oscillations.　We　show　that　the　quasi-static　process　of　the　relaxation　oscillations　can　be　prolonged　in　the　presence　of　amplitude-modulated　excitation.　Then,　a　two-parameter　bifurcation　set　is　plotted　to　investigate　the　transition　of　the　relaxation　oscillations.　In　particular,　we　find　that　the　hysteresis　with　four　fold　points　can　be　split　into　the　one　with　eight　fold　points.　Based　on　this,　dynamical　mechanism　underlying　the　appearance　of　a　compound　relaxation　oscillation　patterns　is　revealed.　Our　study　shows　that　amplitude-modulated　excitation　has　great　effects　on　the　fast-slow　dynamics.