Extensive LDA and quasi-particle calculations have been performed on b
oron nitride (BN) single-wall and multi-wall nanotubes. Strain energie
s are found to be smaller for BN nanotubes than for carbon nanotubes o
f the same radius, owing to a buckling effect which stabilizes the BN
tubular structure. For tubes larger than 9.5 angstrom in diameter, the
lowest conduction band is predicted to be free-electron-like with ele
ctronic charge density localized inside the tube. For these tubes, thi
s band is at constant energy above the top of the valence band. Conseq
uently, contrarily to carbon nanotubes, single- and multi-wall BN nano
tubes are constant-band-gap materials, independent of their radius and
helicity. In addition, we expect them to exhibit remarkable propertie
s under n-type doping.