The possibility to use the axial point group dynamical representations for the infrared and Raman active modes classification in nanotubes is analyzed. The method proposed allows one to obtain the results of phonon symmetry analysis for nanotubes in Mulliken designations, which are traditional for molecules and crystallographic point groups. The approach suggested is applied to the phonon symmetry analysis in the single-wall carbon and MoS₂-based nanotubes. First-principles calculations of phonons in a bulk MoS₂ crystal and a monolayer S-Mo-S are made. The results obtained are in reasonable agreement with the existing experimental data and other published results. The first-principles calculations of the phonon frequencies for armchair and zigzag MoS₂ nanotubes are performed for the first time. It is shown that the number of infrared and Raman active modes becomes fixed starting from the relatively small nanotube diameters. The correlation of the phonon modes of MoS₂ nanotubes with diameters up to 3.64 nm with phonon modes of the S-Mo-S monolayer is analyzed. It is demonstrated that the interpretation of the nature of nanotube A-type modes in the crystallographic factorization of the line group L = TF is the same as for m = 0 modes in the “polymer type” factorization L = ZP where P is the subgroup of the isogonal point group F, T is the translation subgroup of line group and the cyclic group Z includes the one-dimensional translations and the rotations around the screw axes or the reflections in the glide planes.