In　this　paper,　we　use　the　asymptotic　perturbation　method　to　investigate　nonlinear　oscillations　and　chaotic　dynamics　in　a　rotor-active　magnetic　bearings　(AMB)　system　with　8-pole　legs　and　the　time-varying　stiffness.　The　stiffness　in　the　AMB　is　considered　as　the　time　varying　in　a　periodic　form.　Because　of　considering　the　weight　of　the　rotor,　the　formulation　on　the　electromagnetic　force　resultants　includes　the　quadratic　and　cubic　nonlinearities.　The　resulting　dimensionless　equations　of　motion　for　the　rotor-AMB　system　with　the　time-varying　stiffness　in　the　horizontal　and　vertical　directions　are　a　two-degree-of-freedom　nonlinear　system　with　quadratic　and　cubic　nonlinearities　and　parametric　excitation.　The　asymptotic　perturbation　method　is　used　to　obtain　the　averaged　equations　in　the　case　of　primary　parametric　resonance　and　1/2　subharmonic　resonance.　It　is　found　that　there　exist　period-3,　period-4,　period-6,　period-7,　period-8,　quasiperiodic　and　chaotic　modulated　amplitude　oscillations　in　the　rotor-AMB　system　with　the　time-varying　stiffness.　It　is　seen　from　the　numerical　results　that　there　are　the　phenomena　of　the　multiple　solutions　and　the　soft-spring　type　and　the　hardening-spring　type　in　nonlinear　frequency-response　curves　for　the　rotor-AMB　system.　The　parametric　excitation,　or　the　time-varying　stiffness　produced　by　the　PD　controller　is　considered　to　be　a　controlling　force　which　can　control　the　chaotic　response　in　the　rotor-AMB　system　to　a　period　n　motion.