We analyze, via molecular dynamics, the hydrogenation of the smallest zigzag and armchair carbon nanotubes. These tubes with radii smaller than 0.4 nm, contrary to larger tubes, upon exposure to molecular hydrogen have an exothermic hydrogenation. First principles simulations show that these tubes are thermally stable up to temperatures of 1500 K. The free energy profiles for hydrogen abstraction, computed via constrained dynamics for the case of the (2,2) tube, show that the energy barrier for hydrogenation from a single H-2 molecule is about 1.5-2.0 eV, thus amounting to half (or less) the dissociation energy of H-2 in gas phase. (C) 2009 Elsevier B.V. All rights reserved.