An asymptotic method based upon the principles of geometrical optics, which has been used for linear problems, is extended to nonlinear wave propagation in a rotating fluid of variable depth. It yields the same modes, the same phase function, and the same rays as does the linear theory. However along each ray the amplitude satisfies a nonlinear equation of Korteweg‐DeVries form. Thus, the theory combines certain features of the linear theory of short waves and the nonlinear theory of long waves. The theory is developed for a layer of fluid with a free surface or for an atmosphere which extends upward to infinity, and also for fluid in a channel or a waveguide. It may be useful in dealing with problems of geophysical interest.