This work aims to study experimentally the rheology and viscosity of nanofluids based on ethylene glycol, water, and isopropyl alcohol containing single-walled carbon particles (SWCNT). The weight concentration of SWCNTs varied from 0.05 to 1%, the temperature varied within the range from 10 to 50 °C. Sodium dodecylbenzene sulfonate, polyvinylpyrrolidone, and sodium dodecyl sulfate were used as dispersants. All the studied nanofluids were characterized by non-Newtonian rheology, if only the concentration of SWCNTs was not too low. The nanofluids were either pseudoplastic or viscoplastic fluids. With the increasing concentration of SWCNTs, the fluid index decreased, while the consistency factor increased. Moreover, as the CNT concentration increased, pseudoplastic fluids could become viscoplastic. In the general case, the rheology of nanofluids also changed with increasing temperature. An important fact is that the viscosity of the studied nanofluids depends actually on the effective size of the SWCNTs. The greater their effective size, the greater the viscosity. Indirectly, the answer to the question about the reason for this behavior is given by studying the microrheology of these nanofluids. They demonstrate viscoelastic properties of the nanofluids. This behavior is associated with the formation of a solid spatial lattice of nanotubes in the bulk of nanofluid.