We analyze the motion of multiwalled carbon nanotubes clusters in water or ethanol upon irradiation with a 975 and 1550 nm laser beam guided by an optical fiber. Upon measuring the velocities of the nanotube clusters in and out of the laser beam cone, we were able to identify thermophoresis, convection and radiation pressure as the main driving forces that determine the equilibrium position of the dispersion at low optical powers: while thermophoresis and convection pull the clusters toward the laser beam axis (negative Soret coefficient), radiation pressure pushes the clusters away from the fiber tip. A theoretical solution for the thermophoretic velocity, which considers interfacial motion and a repulsive potential interaction between the nanotubes and the solvent (hydrophobic interaction), shows that the main mechanism implicated in this type of thermophoresis is the thermal expansion of the fluid, and that the clusters migrate to hotter regions with a characteristic thermal diffusion coefficient D-T of 9 x 10(-7) cm(2) K-1 s(-1). We further show that the characteristic length associated with thermophoresis is not that of the nanotube clusters size, Omicron(1) mu m, but that corresponding to the microstructure of the clusters, Omicron(1) nm. We finally discuss the role of the formation of gas-liquid interfaces (microbubbles) at high optical powers on the deposition of carbon nanotubes on the optical fiber end faces.