Abstract: On the equat orial β-plane the foundation of zonal semi-geostrophic motion is investigated.It is indicated that, only under the condition that the zonal scale is large, the non-geostrophic wind is dispersed with the disper sion of gravity -inertia wave, and the time conservation of the vorticity is established.The Kelvin wave and Rossby short wave in mixed wave will participate the evolution stage not participate the adjustment stage of motion.