Abstract: For some phenomena of ENSO event,the large scale,low frequency motions are more interesting than other motions. So the longwave,low frequency approximation is adopted in this paper,that is,the zonal motions satisfy the geostrophic equilibrium. Analysis shows that when motion is symmetric about the equator (n=0,2), free waves in the coupled model consist of Kelvin waves and Rossby waves in the ocean and atmos phere respectively. The unstable air-sea coupled waves are excited by wave-wave interaction. Based on the magnitude of the air-sea coupled strength and ε (ratio of the ocean gravity wave velocity to the atmosphere one),the unstable region can be divided into three parts. In the region Ⅰ (ε0.16 and weak air-sea interaction),there exists a eastward propagating unstable coupled wave in the long wave range. In addition,in the region Ⅲ(ε<0.16 and strong air-sea interaction),the unstable coupled waves possess an anomaly physical characteristics. Owing to the large growth rate in the short wave range,it is estimated the unstable coupled wave is quickly broken and changed into the large scale convection. Another unstable wave exists in the long wave range,but its evolution is traced out difficulty from the free waves.Anti-symmetric motions about the equator are discussed.