We have investigated the surface chemistry of coadsorbed hydrogen and halogen atoms on Ge(100), produced by dissociative chemisorption of HCl and HBr, by temperature-programmed desorption. The initial sticking probability S-0 for HCl decreases from 0.6 at a substrate temperature of 270 K to 0.05 at 400 K, indicative of a precursor state to adsorption. For HBr S-0 is constant at 0.7 over the same temperature range. A fraction f of adsorbed hydrogen atoms desorb associatively as H-2 near 570 K, while the remaining (1-f) H atoms recombine with adsorbed halogen atoms and desorb as the hydrogen halide (HX) near 580-590 K. The activation energies for desorption of H-2, HCl, and HBr are all approximately 40 kcal/mol. For both HCl and HBr f is 0.7 at low initial coverage and decreases slightly to 0.6 at saturation. The fraction f of adsorbed halogen atoms left on the surface following the competitive desorption of H-2 and HX desorb as the dihalides GeCl2 and GeBr2 near 675 and 710 K, respectively. Desorption of H-2, HCl, and HBr occurs with near-first-order kinetics, similar to the behavior of hydrogen adsorbed alone, which we attribute to preferential pairing induced by the pi bond on unoccupied Ge dimers. We introduce and solve a generalized doubly occupied dimer model incorporating competitive pairing of H+H, H+X, and X+X on Ge dimers to explain the near-first-order kinetics. The model quantitatively accounts for both the desorption kinetics and the relative yields of H-2 and HX with pairing energies of approximate to 3 kcal/mol. Implications of the present results for surface thermochemistry, chemical vapor deposition, and atomic layer epitaxy of Ge and Si(100)2X1 surfaces are discussed.