Boron nitride (BN) multi-walled (MWNT) or single-walled (SWNT) nanotubes were synthesized from carbon MWNT and SWNT templates, respectively, under heating of C nanotubes together with boron trioxide in a flowing nitrogen atmosphere. B and N atom substitution for C atoms in the nanotubular shells during C oxidation by the B2O3 vapor in the N2 flow is thought to underlie the formation mechanism. Structural and chemical BN MWNT/SWNT analyses were performed by means of high-resolution electron microscopy (HRTEM) and electron energy loss spectroscopy (EELS), respectively. In particular, BN MWNT shell structure and defects, and electron irradiation stability were studied. Finally, the prospects of using the substitution technique for the synthesis of other advanced nanostructures made of BN (nanorods, nanoplates and nanocones) are discussed.