Highly nonlinear pump fluence dependence was observed in the ultrafast one-color pump probe responses excited by 38 fs pulses resonant with the E-22 transition in a room-temperature solution of (6,5) carbon nand tubes. The differential probe transmission (Delta T/T) at the peak of the pump probe response (tau = 20 fs) was measured for pump fluences from similar to 10(13) to 10(17) photons/pulse cm(2). The onset of saturation is observed at similar to 2 x 10(16) photons/pulse cm(2) (similar to 8 x 10(5) excitons/cm). At: pump) fluences > 4 x 10(16) photons/pulse cm(2) (similar to 1.6 x 10(6) excitons/cm), Delta T/T decreases as the pun. p fluence increases. Analogous signal saturation behavior was observed for all measured probe delays. Despite the high. exciton density at saturation, no change in the E-22 population decay rate was observed at short times (< 300 fs). The pump probe signal was modeled by a third-order perturbation theory treatment that includes the effects of inhomogeneous broadening. The observed Delta T/Tsignal is well-fit by a pump-fluence-dependent dephasing rate linearly dependent on the number of exoitons created by the pump pulse. Therefore, the observed nonlinear pump intensity dependence is attributed to the effects of quasi-elastic exciton-exciton interactions on the dephasing rates of single carbon nanotubes. The low fluence total dephasing time is 36 fs, corresponding to a homogeneous Width of 36 meV (290 cm(-1)), and the derived E-22 inhomogeneous width is 68 meV (545 cm(-1)). These results are contrasted with photon-echo-derived parameters for the E-11 transition.