Abstract: In this paper, the high non-linear atmospheric motion is considered as a kind of semi-or quasi-eddy motion. By introducing the method of quasi-eddy approximation, i. e., conserving the eddy terms at the beginning and then ignoring some of them after integrating the equations along the latitude circle, the oscillation equations of certain characteristics of atmospheric motion such as zonal index, zonal mean meridional transport of momentum and vorticity and etc. and their harmonic solutions are obtained. The period of oscillation depends on v2, a measure of the zonal mean meridional kinetic energy. The period of the first harmonic is about 20 days. The results may probably explain to some extent the oscillation of certain zonal mean characteristics of the observed atmospheric motion and the vacillation of experimental simulation. The main scientific purpose of this paper is to demonstrate that non-linear extended atmospheric processes might he also attacked by even the high linear theory.