The　bifurcations　of　multiple　limit　cycles　for　a　rotor-active　magnetic　bearings　(AMB)　system　with　the　time-varying　stiffness　are　considered　in　this　paper.　The　governing　nonlinear　equation　of　motion　is　established　for　the　rotor-AMB　system　with　single-degree-of-freedom　and　parametric　excitation.　Using　the　method　of　multiple　scales,　the　governing　nonlinear　equation　of　motion　is　first　transformed　to　the　averaged　equation,　which　is　in　the　form　of　a　Z　2-symmetric　perturbed　polynomial　Hamiltonian　system　of　degree　5.　Then,　the　bifurcation　theory　of　planar　dynamical　system　and　the　method　of　detection　function　are　utilized　to　analyze　the　bifurcations　of　multiple　limit　cycles　of　the　averaged　equation.　Four　groups　of　parametric　controlling　conditions　are　given　to　obtain　the　configurations　of　compound　eyes.　It　is　found　that　there　exist　respectively　at　least　17,　19,　21　and　22　limit　cycles　in　the　rotor-AMB　system　with　the　time-varying　stiffness　under　the　different　controlling　conditions.　©　2008　World　Scientific　Publishing　Company.