Abstarct: In this study, the buckling and vibration pressurized rotating nano-composite long thin micro-tube, reinforced by CNTs are presented. For analyses of the micro-tube are used modify couple stress theory and Eringen nonlocal elasticity theory, and the results with each other are compared. The results show the effect of various parameters such as angular velocity, temperature and pressure differences between of the inside and outside, the size of the magnetic field, Eringen non-local parameter, material length scale parameter and volume fraction of nano-tubes; on the natural frequency, the critical buckling load, mode shapes vibration and response system. The results obtained show that with increasing volume fraction of nanotubes, thickness, material length scale parameter and magnetic fields, natural frequency and critical buckling load increased but the amplitude responses of system decreases. The difference between two theoretical results show that the modify couple stress theory explains behavior of microtube better than non-local theory. Because non-local parameter has no effect on the results and doesn't fit to justify the behavior of micro tubes, but changing the material length scale parameter shows addition of the reinforcing as good. The results in the optimization of micro-structures for manufacturing sensors, displacement fluid and drug delivery will be very useful.