A strong solar cycle variation in hydrogen and deuterium densities is observed in the nightside thermosphere of Venus when Pioneer Venus Orbiter (PVO) measurements made during the first three Venus years of the mission are compared with those made during the preentry phase of the mission. Solar maximum conditions prevailed during the former period, while near solar minimum conditions occurred during the latter. Pronounced density enhancements in H of 6.5 times and D of 4 times are observed in the nightside bulge region as solar activity decreased from maximum to near-minimum values. We attribute the buildup of H and D to a reduction in the escape fluxes as solar activity decreased, a behavior that is consistent with the known properties of the dominant escape processes due to the charge separation electric field (E) and charge exchange (CE). Application of this simple concept leads to expressions for the H and D escape fluxes which relate solar cycle variations of the respective bulge densities and escape fluxes to the dayside source fluxes. Planet averaged escape fluxes in the ranges 1.23¿107 cm-2 s-1≤&PHgr;¿e(H)≤1.45¿107 cm-2 s-1 and 1.61¿105 cm-2 s-1≤&PHgr;¿e(D)≤2.15¿105 cm-2 s-1 are obtained by this method without specifying any particular escape mechanism. Considering the uncertainties in the measured parameters, these flux ranges are in reasonable agreement with the escape fluxes derived from the specific processes, E and CE. When fractionation without or with an external source of water (e.g., comets) is applied to the range of possible escape fluxes, a fractionation factor f=0.44 is obtained and an ancient reservoir of water equivalent to the range 125 m to 570 m of liquid uniformly distributed on the surface or 3.7% to 17% of a full terrestrial ocean is derived. When the specific escape processes E and E+CE are considered, the f values are 0.15 and 0.1 and the magnitudes of the reservoirs are lower, having a range of equivalent depths of 4.1 m to 36.8 m, respectively. ¿ American Geophysical Union 1996