The chemical shifts from the protons belonging to surfactants differing only by the nature of counterions (Li, Na, Cs) are considered in their interaction with the surface of carbon nanotubes. It was shown that the dominant mechanisms of interaction of the surfactant molecules with the nanotubes surface in aqueous solutions depend on the nature of counterions. In particular, sodium dodecyl sulfate molecules interact with the nanotubes surface mainly by their head groups instead of tail groups, and thus it can be assumed that the surface of nanotubes can be coated with a layer of flattened micelles. In the other cases, a structureless random adsorption of surfactant molecules with partially ordered arrangement of head and tail groups, incompact for the molecules of lithium dodecyl sulfate or cling swarm round for the molecules of cesium dodecyl sulfate is more likely.