We report a femtosecond transient absorption spectroscopic study on the (6, 5) single-walled carbon nanotubes and the (7, 5) inner tubes of a dominant double-walled carbon nanotube species. We found that the dynamics of exciton relaxation probed at the first transition-allowed state (E(11)) of a given tube type exhibits a markedly slower decay when the second transition-allowed state (E(22)) is excited than that measured by exciting its first transition-allowed state (E(11)). A linear intensity dependence of the maximal amplitude of the transient absorption signal is found for the E(22) excitation, whereas the corresponding amplitude scales linearly with the square root of the E(11) excitation intensity. Theoretical modeling of these experimental findings was performed by developing a continuum model and a stochastic model with explicit consideration of the annihilation of coherent excitons. Our detailed numerical simulations show that both models can reproduce reasonably well the initial portion of decay kinetics measured upon the E(22) and E(11) excitation of the chosen tube species, but the stochastic model gives qualitatively better agreement with the intensity dependence observed experimentally than those obtained with the continuum model.