A method is presented for calculating the nonlinear properties and effects of internal acoustic-gravity waves. This method is referred to as perturbed orbits or modified orbits and has been widely used in theories of plasma waves. The basis of this method is to express nonlinear wave oscillation in terms of the orbits of the particles of the medium. The task of calculating nonlinear wave effects is thus transformed to calculating particle orbits. The latter task is simplified by the use of elementary statistical techniques such as cumulant expansions. The method of perturbed orbits is also closely related to the direct interaction approximation, which has been so useful in theories of fluid turbulence. This method is applied to calculate the nonlinear saturation (self-limited) amplitude of atmospheric gravity waves. Here, saturation amplitude refers to the amplitude of gravity waves above which nonlinearities are strong enough to stop the wave from growing with height. The saturation amplitude is the largest amplitude a gravity wave spectrum can attain. The present results for the saturation amplitude are compared with gravity wave amplitudes observed in the mesosphere. A calculation is also made of the enhancement of atmospheric diffusion by gravity waves. The enhanced diffusion coefficient plays an important role in the present theory, and its predicted value is consistent with observations of enhanced transport in the mesosphere.