The　asymptotic　perturbation　method　is　used　to　analyze　the　nonlinear　vibrations　and　chaotic　dynamics　of　a　rotor-active　magnetic　bearing　(AMB)　system　with　16-pole　legs　and　the　time-varying　stiffness.　Based　on　the　expressions　of　the　electromagnetic　force　resultants,　the　influences　of　some　parameters,　such　as　the　cross-sectional　area　A　alpha　of　one　electromagnet　and　the　number　N　of　windings　in　each　electromagnet　coil,　on　the　electromagnetic　force　resultants　are　considered　for　the　rotor-AMB　system　with　16-pole　legs.　Based　on　the　Newton　law,　the　governing　equation　of　motion　for　the　rotor-AMB　system　with　16-pole　legs　is　obtained　and　expressed　as　a　two-degree-of-freedom　system　with　the　parametric　excitation　and　the　quadratic　and　cubic　nonlinearities.　According　to　the　asymptotic　perturbation　method,　the　four-dimensional　averaged　equation　of　the　rotor-AMB　system　is　derived　under　the　case　of　1　:　1　internal　resonance　and　1　:　2　subharmonic　resonances.　Then,　the　frequency-response　curves　are　employed　to　study　the　steady-state　solutions　of　the　modal　amplitudes.　From　the　analysis　of　the　frequency　responses,　both　the　hardening-type　nonlinearity　and　the　softening-type　nonlinearity　are　observed　in　the　rotor-AMB　system.　Based　on　the　numerical　solutions　of　the　averaged　equation,　the　changed　procedure　of　the　nonlinear　dynamic　behaviors　of　the　rotor-AMB　system　with　the　control　parameter　is　described　by　the　bifurcation　diagram.　From　the　numerical　simulations,　the　periodic,　quasiperiodic,　and　chaotic　motions　are　observed　in　the　rotor-active　magnetic　bearing　(AMB)　system　with　16-pole　legs,　the　time-varying　stiffness,　and　the　quadratic　and　cubic　nonlinearities.