The magnitude of the third-order nonlinear polarizability &ggr; of armchair nanotube is theoretically studied. The calculated results for theC70tube are consistent with those measured by Neher &etal; [Opt. Lett.17, 1491 (1992)]. The static and dynamical magnitudes of &ggr; can be greatly enhanced by increasing the carbon number. When the carbon number is big enough, the major dynamical response peaks with large &ggr; magnitudes are located at the optical frequency &ohgr; near the energy gapEg(i.e.,3&ohgr;∼3Eg), and the highest peak magnitude is much larger than that ofC70,which is important in practical use. ©1997 American Institute of Physics.