  Nonlinear transmission of 80 and 140 femtosecond pulsed light with $0.79 \mu
m$ wavelength through single walled carbon nanotubes suspended in water
containing sodium dodecyl sulphate is studied. Pulse-width independent
saturation absorption and negative cubic nonlinearity are observed,
respectively, in open and closed aperture Z-scan experiments. The theoretical
expressions derived to analyze the z-dependent transmission in the saturable
limit require two photon absorption coefficient $\beta_0\sim$ $1.4 cm/MW$ and a
nonlinear index $\gamma \sim -5.5 \times10^{-11} cm^2/W$ to fit the data.
