The nonlinear equations governing the propagation of acoustic-gravity waves in a moist atmosphere are derived following the theory of mixtures. The water droplets are assumed to be very small compared to the characteristic scales of the system and numerous enough to treat them as a fluid. The atmosphere is assumed saturated at all heights, and the equations are linearized about a background with no shear flow. The WKB solution reveals that the local properties of the atmosphere are considerably affected by the exchange of heat due to condensation or evaporation. In particular, for a given frequency and horizontal wavelength, the vertical wavelength increases compared to the case of a dry atmosphere. The treatment applies to all frequencies less than the audible range.