Spin multiplicity enhancements of third-order nonlinear polarizabilities have been investigated at the excited state for finite single-walled carbon nanotubes (5,0) and (6,0) in terms of the time-dependent density functional theory combined with the sum-over-states method. The time-dependent density functional theory at the B3LYP/3-21G level is employed to calculate the transition moments and the excited state energies of optimized tubes. The obtained results show that the third-order polarizabilities of gamma at the excited triplet state are enhanced about from 2 to 3 orders of magnitude and the estimated third-order optical susceptibility of chi((3)) is as large as 10(-8) esu magnitude order. The electron transitions among the three triplet states make significant contributions to third-order polarizabilities of the (5,0) nanotube, and the electron transition between the two triplet states makes main the contribution to those of the (6,0) nanotube. (C) 2003 American Institute of Physics.