In this work, one-dimensional graphane nanotubes (GN, stoichiometry CH), built from 2D single-sheet graphanes, are explored theoretically. Zigzag type GN(10,0) and armchair type GN(10,10) structures with varying surface termination were investigated in detail. GN(10,10)-A is found to be the most stable configuration among the GN structures considered. An annealing analysis indicates that graphane-A and GN(10,10)-A are likely to be stable at elevated temperature. A possible reaction path to GN(10,10)-A is suggested by the reaction of single-walled carbon nanotube (10,10) + H(2); the indications are that the GN(10,10)-A can be made at low temperature and high partial pressure of H(2) gas from the corresponding nanotube. The graphane nanotubes are predicted to be wide band gap insulators. A study of the effect of the diameter of GN structures shows, unexpectedly, that the gap increases on reducing the diameter of the graphane nanotubes. We also investigated several partially hydrogenated graphenes and single-walled carbon nanotubes (SWNT); the greater hydrogenation is, the more stable is the resulting structure. The band gap of graphene or SWNT can be tuned via hydrogenation.