Abstract: From the quasi-geostrophic two-layer model,the quasi-resonance occurs possibly for two cases:(1)pure barotropic waves (2)two baroclinic waves and one barotroPic wave.For case(2),it is the analytic solution of triad amplitude of quasi-resonance and approximate exPression for variation Period of wave energy which are found.Both the annroximate exoression numerical calculation indicate that for the barnclinic atmosphere the Period of energy variaton aPProaches the Period 2πε/Δω corresponding to the quasi-resonance frequency mismatch Δω itself more easily than for the barotropic atmosphere.It is Pointed from Physics that there is a feedback mechanism between the phase of wave and wave amplitude,the slowly varying phase difference between the barotropic wave and the baroclinic waves causes the transformation of the kinetic energy and the available potential energy,and formes the low-frequency oscillation alternately strengthening and weakening the barotropic wave and the baroclinic wave,which oscillation period is the same as above approximate formula.