The two sets of commensurate double-walled boron nitride and titania hexagonally-structured nanotubes (DW BN and TiO₂ NTs) possessing either armchair- or zigzag-type chiralities have been considered, i.e., (n ₁,n₁) at (n₂,n₂) or (n ₁,0) at (n₂,0), respectively. For symmetry analysis of these nanotubes, the line symmetry groups for one-periodic (1D) nanostructures with rotohelical symmetry have been applied. To analyze the structural and electronic properties of hexagonal DW NTs, a series of large-scale ab initio DFT-LCAO calculations have been performed using the hybrid Hartree-Fock/Kohn- Sham exchange-correlation functional PBE0 (as implemented in CRYSTAL-09 code). To establish the optimal inter-shell distances within DW NTs corresponding to the minima of calculated total energy, the chiral indices n₁ and n₂ of the constituent single-walled (SW) nanotubes have been successively varied.