The hydrogen recombination reaction, H + H --> H-2, and the hydrogen exchange reaction, H + H-2--> H-2 + H, taking place inside single-walled carbon nanotubes have been studied by using quantum mechanics molecular dynamics simulations. Two types of hydrogen exchange reactions have been found. The fast reaction lasts in less than 5 fs, and the slow one lasts for about 40 fs with a clear intermediate state manifested. The collisional reaction for two H atoms to form a H-2 molecule usually takes place in a time interval of 25 fs. We also describe the detailed process of the reaction of individual H atoms to form H-2 molecules and, with an increase of the density of H, molecules confined in the tubes, H-2 molecular condensation to form clusters and finally to form condensed H-2 molecular lattices.