Multimode　damping　of　a　stay　cable　attached　with　a　negative　stiffness　device　(NSD)　and　a　linear　hysteretic　damper　was　studied.　The　frequency　equation　of　a　cable　under　transverse　control　forces　at　two　locations　is　used　for　damping　analyses　by　considering　arbitrary　NSD　and　damper　locations.　The　effects　of　NSD　and　damper　locations,　damper　parameters　and　negative　stiffness　values　on　multimode　damping　of　stay　cable　are　examined.　It　can　be　found　that　the　multimode　cable　damping　values　can　be　significantly　enhanced　comparing　with　the　single　linear　hysteretic　damper.　The　closer　the　installation　locations,　the　higher　the　damping　level.　Furthermore,　multimode　damping　effect　of　the　combinations　is　verified　by　using　a　long　stay　cable　installed　with　a　viscous　shear　damper　on　the　Sutong　Bridge,　together　with　an　inertial　damper.　The　feasibility　of　the　NSD　is　carefully　discussed.　The　results　show　that　the　NSD　is　more　helpful　to　enhance　the　multimode　damping　comparing　with　the　inertial　damper.　©　2022,　Editorial　Department　of　Journal　of　Hunan　University.　All　right　reserved.