A comprehensive one-dimensional photochemical model extending from the middle atmosphere (50 km) to the exobase (432 km) has been used to study the escape of hydrogen and deuterium from the Earth's atmosphere. The model incorporates recent advances in chemical kinetics as well as atmospheric observations by satellites, especially the Atmosphere Explorer C satellite. The results suggest: (1) the escape fluxes of both H and D are limited by the upward transport of total hydrogen and total deuterium at the homopause (this result is known as Hunten's limiting flux theorem); (2) about one fourth of total hydrogen escape is thermal, the rest being nonthermal; (3) escape of D is nonthermal; and (4) charge exchange and polar wind are important mechanisms for the nonthermal escape of H and D, but other nonthermal mechanisms may be required. The efficiency to escape from the terrestrial atmosphere for D is 0.74 of the efficiency for H. If the difference between the D/H ratio measured in deep-sea tholeiite glass and that of standard sea water, delta D = -77%, were caused by the escape of H and D, we estimate that as much water as the equivalent of 36% of the present ocean might have been lost in the past.