Based　on　the　Timoshenko　beam　theory,　this　paper　proposes　a　nonlocal　bi-gyroscopic　model　for　spinning　functionally　graded　(FG)　nanotubes　conveying　fluid,　and　the　thermal-mechanical　vibration　and　stability　of　such　composite　nanostructures　under　small　scale,　rotor,　and　temperature　coupling　effects　are　investigated.　The　nanotube　is　composed　of　functionally　graded　materials　(FGMs),　and　different　volume　fraction　functions　are　utilized　to　control　the　distribution　of　material　properties.　Eringen＇s　nonlocal　elasticity　theory　and　Hamilton＇s　principle　are　applied　for　dynamical　modeling,　and　the　forward　and　backward　precession　frequencies　as　well　as　3D　mode　configurations　of　the　nanotube　are　obtained.　By　conducting　dimensionless　analysis,　it　is　found　that　compared　to　the　Timoshenko　nano-beam　model,　the　conventional　Euler-Bernoulli　(E-B)　model　holds　the　same　flutter　frequency　in　the　supercritical　region,　while　it　usually　overestimates　the　higher-order　precession　frequencies.　The　nonlocal,　thermal,　and　flowing　effects　all　can　lead　to　buckling　or　different　kinds　of　coupled　flutter　in　the　system.　The　material　distribution　of　the　P-type　FGM　nanotube　can　also　induce　coupled　flutter,　while　that　of　the　S-type　FGM　nanotube　has　no　impact　on　the　stability　of　the　system.　This　paper　is　expected　to　provide　a　theoretical　foundation　for　the　design　of　motional　composite　nanodevices.