Spillover of hydrogen on nanostructured carbons is a phenomenon that is critical to understand in order to produce efficient hydrogen storage adsorbents for fuel cell applications. The spillover and interaction of atomic hydrogen with single-walled carbon nanotubes (SWNTs) is the focus of this combined theoretical and experimental work. To understand the spillover mechanism, very low occupancies (i.e., 1 and 2 H atoms adsorbed) on (5,0), (7,0), (9,0) zigzag (semiconducting) SWNTs and a (5,5) anrichair (metallic) SWNT, with corresponding diameters of 3.9. 5.5, 7.0, and 6.8 angstrom, were investigated. The adsorption binding energy of H atoms depends on H occupancy, tube diameter, and helicity (or chirality), as well as endohedral (interior) vs exohedral (exterior) binding. Exohedral binding energies are substantially higher than endohedral binding energies due to easier sp(2)-sp(3) transition in hybridization of carbon on exterior walls upon binding. A binding energy as low as -8.9 kcal/mol is obtained for 2H atoms on the exterior wall of a (5, 0) SWNT. The bindiner energies of H atoms on the metallic SWNT are significantly weaker (about 23 kcal/mol weaker) than that on the semiconductor SWNT, for both endohedral and exohedral adsorption. The binding energy is generally higher on SWNTs of larger diameters, while its dependence on H occupancy is relatively weak except at very low occupancies. Experimental results at 298 K and for pressures up to 10 MPa with a carbon-bridged composite material containing SWNTs demonstrate the presence of multiple adsorption sites based on desorption hysteresis for the spiltover H on SWNTs, and the experimental results were in qualitative agreement with the molecular orbital calculation results.