It is proved, based on the quasi--geostropic barotropic vortex equation and the quasi-resonance conditions K1+ K2+ K3=0 and ω1 +ω1 +ω3 =Δω, that the analytic solution ofthe 3--wave amplitude of quasi--resonance is an elliptical function. The approximate expressionfor the periodic variation of wave energy is thus obtained under certain conditions. Boththe approximate expression and numerical calculation indicate that the period of energyvariation approaches the period 1/Δω corresponding to the quasi--resonance frequency biasΔω itself. When Δω～（0.1--0.025）o（ωj）, the energy variation period is 12---46 days andwhen Δω=0, it is 25--568 days. Therefore, the occurrence of frequency bias Δω is probablya new important mechanism for the formation of mid-latitude low--frequency oscillation.This also accounts for the result of the numerical test Egger （1978） did on blocking causedby the resonance of two topographic stationary waves and one free slow wave.
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