The physisorption and chemisorption of hydrogen in BN nanotubes, investigated by density functional theory (DFT), were compared with carbon nanotubes. The physisorption of H-2 on BN nanotubes is less favorable energetically than on carbon nanotubes; BN nanotubes cannot adsorb hydrogen molecules effectively in this manner. Chemisorption of H-2 molecules on pristine BN nanotubes is endothermic. Consequently, perfect BN nanotubes are not good candidates for hydrogen storage by either mechanism. Other strategies must be utilized if BN nanotubes are to be employed as hydrogen storage media such as utilizing them as supporting media for hydrogen-absorbing metal nanoclusters.