We performed a study of the molecular adsorption of hydrogen on BN nanotubes. We present ab initio calculations for the linear optical response of single wall zigzag BN(6,0) nanotubes as a function of the hydrogen adsorption on the exterior surface of the nanotube. The calculation of the linear optical response is performed by using density functional theorywith the use of plane waves and pseudopotentials. We consider four different nanotube‐structures adsorbed with different coverage of molecular hydrogen.We find optimized atomic coordinates for such structures and calculate binding energies for the molecule of hydrogen on the nanotube.After having the linear response of the considered structures, we have calculated their energy loss function spectra. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)