The first-principles simulations were performed to investigate the structure and properties of single-wall nanotubes constructed from the binary MX and mixed M2XY, MLX2 or MLXY (M, L = Ga, In, M ≠ L; X, Y= S, Se, Te, X ≠ Y) monolayers. Different types of parent monolayers, chirality and diameters of nanotubes have been considered. The simulation of Janus nanotubes based on post-transition metal chalcogenides has been performed for the first time. The stability of nanotubes was analyzed both with respect to bulk phases and with respect to monolayers. It is found that the monolayers of monoclinic phase may be preferable for folding of nanotubes in the case of GaTe. On the other hand, the Janus nanotubes possess the lower formation energy than their binary (pristine) counterparts if the heaver chalcogen atom is located on the external nanotube surface. The calculation of the electronic properties also indicates the promise of Janus nanotubes for photocatalytic applications. Young's and shear moduli, as well as Poisson ratios have been estimated for binary and mixed gallium chalcogenide nanotubes for the first time. Analysis of elastic properties of nanotubes based on gallium chalcogenides shows that they have lower rigidity than nanotubes based on transition metal chalcogenides.