The atomic nature of hydrogen storage in single wall carbon nanotubes (SWNTs) has been investigated by thermal desorption spectroscopy utilizing mass spectrometry. The partial pressures of desorbed H2, D2, and HD have been simultaneously recorded after sample loading with a 1:1 mixture of H2 and D2 gases. The amount of desorbed HD molecules approaches the ratio 2:1:1 for HD:H2:D2 in the case of atomic storage, i.e. chemisorption. In the case of storage as molecules, i.e. physisorption, the concentration of HD approaches the background level. Hydrogen isotopes are absorbed as atoms in SWNT samples containing transition metals from either sample production (Ni, Fe, …) and/or activation (opening) process (Ni, Fe, Ti, …). Purified SWNTs adsorb hydrogen molecules at low temperatures.