This　study　aims　to　propose　a　coupled　controller　of　tuned　mass　damping　(TMD)　and　nonlinear　energy　sink　(NES)　for　enhancing　the　stability　and　suppressing　nonlinear　vibrations　of　slender　structures,　such　as　tall　buildings　subjected　to　cross　airflows.　The　nonlinear　governing　equations　are　established　to　describe　the　coupled　vibrations　of　the　slender　structure　with　the　controller.　Subsequently,　a　linear　analysis　is　performed　to　indicate　the　positive　effect　of　proposed　controllers　on　increasing　the　onset　speed　of　galloping　for　the　slender　structure.　A　nonlinear　analysis　is　conducted　to　state　the　mechanism　of　controllers　on　reducing　oscillations　of　the　slender　structure.　The　results　show　that　the　coupled　controller　has　better　effects　on　whether　enhancing　the　onset　speed　or　oppressing　the　structure＇s　vibration　amplitudes.　A　parametric　analysis　is　then　carried　out　to　design　an　optimal　coupled　controller.　The　distributed　controllers　are　designed　in　the　structure,　indicating　that　there　is　an　optimal　number　for　the　controller　where　the　onset　speed　is　peak　depending　on　the　mass　ratio.　The　present　study　can　provide　beneficial　guidance　and　design　for　controlling　the　cross-flow-induced　vibrations　of　slender　structures　in　engineering　applications.