In this work we report on the preparation of some aqueous graphene oxide (GO) dispersions and the investigation of their nonlinear optical response under visible (532 nm) and infrared (1064 nm), picosecond and nanosecond laser excitation. The GO colloids were prepared under specific and well-defined conditions resulting in finely dispersed heavily oxidized large GO sheets. In all cases, GO colloids were found to present large nonlinear absorption and negligible nonlinear refraction. The physical mechanisms responsible for their nonlinear optical response are discussed. In addition, the so-prepared GO dispersions were found to exhibit large broadband optical power limiting action for both pulse durations, comparable to that of C60 for visible laser pulses and much superior for infrared ones.