The mechanisms leading to desorption of molecular hydrogen from Si(100)-2 x 1 and Si(111)-7 x 7 surfaces have been elucidated and refined by detailed examination of the thermal desorption kinetics with particular emphasis on low and very low coverages. In the case of hydrogen desorption from Si(100)-2 x 1, a lattice-gas model incorporating the interactions that are responsible for pairing and clustering of adsorbed hydrogen atoms has been employed to fit temperature programmed desorption (TPD) peaks resulting from initial coverages between 0.01 and 1.0 monolayer (ML). From analysis of our low coverage data, we find that the pairing and clustering energies are (3.2 +/- 0.3) kcal mol(-1) and (3.4 +/- 0.5) kcal mol(-1), respectively. A subtle shift of the TPD peak maximum position as the initial coverage increases from 0.2 to 1.0 ML indicates that the pre-exponential factor and activation energy are weakly coverage dependent. me discuss how this is consistent with coupling of a dihydridelike transition state to its neighbors. The rate of molecular hydrogen desorption from Si(111)-7 x 7 is found to be very nearly second order in total hydrogen coverage when the initial coverage is low. This result is consistent with a two site model involving preferential adsorption of hydrogen atoms at rest atom sites rather than adatom sites.