We have investigated, using dispersion corrected DFT methods, the structure and the spectroscopic properties of carbon buckyonions C60@C180 and C60@C240. C60, C180 and C240 showed a noticeable variation of their geometries in C60@C180 and C60@C240, upon encapsulation. Inclusion of the dispersion correction term in the calculations has a significant effect on the geometry. C60@C180 has a large positive interaction energy, while for C60@C240 a negative value is found indicating that only C240 can easily accommodate C60. In both cases dispersion interactions strongly contribute to the stabilization of the complexes. Vibrational frequencies, electronic transitions and NMR properties have been computed. The results show that encapsulation leads to appreciable variation in the characteristic resonances thus offering a useful tool for a spectroscopic identification of these species.