<p>The first-principles study is performed for the first time of the structure and stability of TiS2 and ZrS2 nanotubes (NTs) in comparison to each other and to similar oxide nanotubes. The hybrid HF-KS PBE0 calculations are made within the scope of the LCAO approximation by means of the CRYSTAL-2009 computer code. To the best of our knowledge, all previous theoretical modelling of tubular disulfides is based on the semiempirical DFTB technique. Transition metal disulfides are known to exist in two modifications 1T and 2H with octahedral and trigonal prismatic coordination of metal atoms, respectively. The applied method allows us to reproduce the experimental properties of the stable 1T phase in good quality. The 3- plane (O-A-O) hexagonal (001) layers from both phases have been used to construct the tubular structures. The possibility of folding the layers from the other presumptive phases with different (cubic, tetragonal and orthorhombic) morphology has also been analysed. The full optimization of all atomic positions has been performed to determine the most favourable nanostructures. Our calculations on single-walled TiS2 and ZrS2 nanotubes confirmed that the NTs obtained by rolling of the hexagonal crystalline layers with octahedral 1T coordination are the most stable. Besides of the NTs with hexagonal morphology, it is possible to obtain the relatively stable NTs with lepidocrocite morphology by rolling up layers of the metastable marcasite-like orthorhombic phase. The strain energy of 1T NTs is almost the same for titanium and zirconium disulfides and obeys the classical 1/R2 law. In spite of the fact that the strain energy of sulfide NTs is greater than that of the similar oxide NTs, the formation energy of the formers is considerably less than the formation energy of latters. Both TiS2 and ZrS2 NTs exhibit properties of the narrow gap semiconductors with the calculated band gap between 1.5 and 2.5 eV.</p>