The spin- and deformation-dependent electron structures of the single-walled chiral and achiral N nanotubes are investigated using a relativistic linear augmented cylindrical wave method. It is shown that the Fermi level separates the valence and conduction band curves. The nanotubes are semimetallic. The spin-orbit coupling results in a splitting of dispersion curves equal up to 0.5 eV. The torsional, uniaxial, and uniform strain results in a drastic change of the electronic states at the Fermi level. The mechanical deformation of some N nanotubes can induce a formation minigaps in a terahertz region that can be used in electronic devices.