Carbon nanotubes have unique properties and applications in various fields such as nonlinear optics, flexible electronics, biocompatible composites for tissue repair, etc. The properties of carbon nanotubes can be tuned when exposed to laser radiation. The manifestation of nonlinear absorption properties can improve the methods of formation and processing of materials containing carbon nanotubes. In this work, the properties of nonlinear absorption in the ultraviolet (355 nm) and visible (532 nm) ranges depending on the type of carbon nanotubes and the type of solvent are investigated. The study was performed using the Z-scan method with pulsed exposure (pulse duration is 20 ns). It was shown that the homogeneity of the carbon nanotubes distribution in a liquid medium affects the nonlinear absorption of laser radiation. Single-walled carbon nanotubes in dimethylformamide showed the best nonlinear absorption coefficient and the lowest threshold fluence when the interaction of the medium with laser radiation becomes nonlinear. The demonstrated laser stability of nanotubes also makes them a promising material for laser radiation limiters and nonlinear optical switchers.