The structure of boron–nitride nanotubes (BNNTs) is very similar to that of CNTs, and they exhibit many similar physical and chemical properties]. In particular, a single walled boron nitride nanotube (BNNT) and a single walled carbon nanotube (CNT) have been reported. The spectral moment's method (SMM) was shown to be a powerful tool for determining vibrational spectra (infrared absorption, Raman scattering and inelastic neutron-scattering spectra) of harmonic systems. This method can be applied to very large systems, whatever the type of atomic forces, the spatial dimension, and structure of the material. The calculations of vibrational properties of BNNT@CNT double-walled hybrid nanostructures are performed in the framework of the force constants model, using the spectral moment's method (SMM). A Lennard–Jones potential is used to describe the van der Waals interactions between inner and outer tubes in hybrid systems. The calculation of the BNNT@CNT Raman active modes as a function of the diameter and chirality of the inner and outer tubes allows us to derive the diameter
dependence of the wave number of the breathing-like modes, intermediate-like modes and tangential-like modes in a large
diameter range. These predictions are useful to interpret the experimental data.