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We present calculations for the optical absorption spectra of hexagonal boron nitride (hBN) and BN nanotubes, using many-body perturbation theory. Solution of the Bethe-Salpeter equation for hBN leads to optical absorption and loss spectra where the positions and shapes of the peaks are strongly dominated by excitonic effects. The binding energy of the first exciton is about 0.71 eV. Comparison of the calculations with recently measured optical absorption and EELS demonstrates that DFT underestimates the “true” band gap of BN by 2.25 eV. This band gap difference can be partially (bot not completely) reproduced by a calculation of the quasi-particle band-structure on the level of the GW-approximation. We show, how the lower dimensionality of BN nanotubes leads to a much stronger excitonic binding energy and at the same time to a larger quasi-particle gap. This leaves the position of the first absorption peak almost unchanged. However, the difference in the series of excitonic peaks allows the spectroscopic distinction between BN nanotubes and bulk BN. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]