The propagation characteristics of plane acoustic-gravity waves in an atmosphere in diffusive equilibrium are studied by using a two-field model which takes into account the collisional transfer of both momentum and energy between species. At wave periods of less than the shortest characteristic diffusion time for the minor gas, significant amplitude and phase differences between the wave-induced density fluctuations of individual gases occur because of the different scale heights of the gases. At longer periods, diffusion induced by the wave acts to eliminate these amplitude. and phase differences and restore the perturbed fluid to diffusive equilibrium. Vertical diffusion is most important as large scale sizes, but horizontal diffusion dominates for horizontal wavelengths of less than several hundred kilometers. As a result of wave-induced diffusion, Al-C satellite measurements of neutral density fluctuations of thermospheric consistituents at 215-km altitude are only compatible with internal gravity waves with periods of ?5--30 min, horizontal wavelengths of ~150--400 km, and downward phase propagation. Diffusion increases in importance with altitude, but is significant for periods of >30 min even at 150-km altitude. Velocity and temperature differences for acoustic-gravity waves are greatest at periods near the mean collision time and diffusion time. Vertical velocity differences between species can be as large as 40% in amplitude and 17¿ in phase at 215-km altitude. Temperature perturbation differences are much smaller but can reach 17% in amplitude and 6.5¿ in phase at 300-km altitude. Two outer solutions to the governing equations, which may be called diffusion waves, have properties drastically different from the acoustic-gravity wave solutions, including order-of-magnitude amplitude differences and close to 180¿ phase differences between the density, velocity, and temperature perturbations of the two species at most periods. Because of the velocity and temperature differences between species, dissipation of wave energy will occur. Damping of acoustic-gravity waves is most significant at periods comparable to the mean collision and diffusion times and can be as large as 50--60% per wave cycle. This effectively filters out those waves with periods long enough to be affected by diffusion except when the observation is near the wave source. The predictions of the theory are consistent with a high-latitude, lower-altitude source like Joule heating or particle precipitation for the medium-scale waves and a more localized random source for the smaller-scale waves observed by AE-C.