The　relation　between　singular　points　and　the　number　of　limit　cycles　is　investigated　for　a　rotor-active　magnetic　bearings　system　with　time-varying　stiffness　and　single-degree-of-freedom.　The　averaged　equation　of　the　system　is　a　perturbed　polynomial　Hamiltonian　system　of　degree　5.　The　dynamic　characteristics　of　the　unperturbed　system　are　first　analyzed　for　a　certain　parameter　group.　The　number　of　limit　cycles　and　their　configurations　of　the　perturbed　system　under　eight　different　parametric　groups　are　obtained　and　the　influence　of　eight　control　conditions　oil　the　number　of　limit　cycles　is　studied.　The　results　obtained　here　will　play　an　important　leading　role　in　the　study　of　the　properties　of　nonlinear　dynamics　and　control　of　the　rotor-active　magnetic　bearings　system　with　time-varying　stiffness.　(C)　2007　Elsevier　Ltd.　All　rights　reserved.