At present, interstellar molecular hydrogen is incapable of detection, although a high abundance has been suspected for almost two decades. In the present paper, an analysis is given of the various processes which determine the molecular concentration in H I clouds. The most important mechanism for forming molecular hydrogen is association on the surface of the interstellar grains, the characteristic time for conversion to molecular form being about 100 years. It is shown that the range of grain temperatures where this recombination reaction is efficient is coincident with the range K, which is expected to resuit from the interaction with the interstellar radiation field. It is estimated that the efficiency (recombination coefficient) of the process is between 0.1 and 1. Regarding dissociative processes, photodissociation through the forbidden transition between the two Heitler-London states of the molecule, previously thought to be most important, is shown to be negligible. Ionization and dissociation of a cloud by random encounters with 0 and B stars occurs about once every 100 years, so that if the grain recombination process is operative, a balance results in which the molecular abundance is roughly comparable with the observed atomic concentration. The cooling properties of molecular hydrogen are discussed.