As　techniques　develop,　the　AMBs　are　more　widely　utilized　in　engineering　fields　than　ever　before.　Their　performance　depends　on　the　actively　control　strategies　due　to　their　complicated　dynamical　characteristics,　which　mainly　arise　from　the　electromagnetic　forces.　Those　forces　usually　are　nonlinear　functions　of　the　displacements　of　the　rotor　and　the　control　current.　An　understanding　of　the　dynamical　characteristics　of　these　structural　systems　is　essential　for　the　rules　of　their　designing　and　controlling.　Variations　of　a　long　time　could　be　observed　easier　with　a　quicker　time　scale.　In　order　to　study　the　AMBs＇　action　during　a　very　long　time,　we　use　the　perturbation　method　to　obtain　the　AMBs＇　motion　up　to　second-order　time　scale.　In　present　work,　the　horizontal　and　vertical　motions　of　a　rotor-AMBs　system　with　8-pole　legs　and　the　time-varying　stiffness　are　formulated.　We　use　the　multiple　scales　method　to　study　the　simultaneous　resonance　of　a　1:2　sub-harmonic　resonance　and　a　primary　parametric　resonance　for　this　system　up　to　the　second-order　time　scale.　With　numerical　simulation,　we　focus　on　the　nonlinear　dynamics　describing　the　system＇s　approximate　solution　with　regard　to　the　second-order　time　scale.　It　is　found　that　the　modulations　of　the　amplitudes　and　phases　of　the　rotor-AMBs　system　in　higher　time　scale　could　be　severely　affected　by　changing　some　parameters　in　governing　equations.　Copyright　©　2013　by　ASME.