Optical limiting properties of singlewall carbon nanotubes suspended in water have been evaluated with 7 ns pulses at 532 and 1064 nm and compared with those of other materials. In order to determine the origin of optical limiting, we carried out a Z-scan experiment at 532 nm and 1064nm at different input energies. We evidenced strong nonlinear scattering and a refractive effect with a negative nonlinear index. The kinetics of nonlinear transmission, from the nanosecond to millisecond time scale, was studied using a pump-probe set-up at 1064nm. We observed cavitation bubbles growth at low input energy. The different nonlinear effects evidenced are discussed in terms of physical origin and in terms of broadband optical limiting efficiency.