Abstract: Wind tunnel tests on aircraft models often demonstrate that the variation of lateral-directional rolling and yawing moments with the yaw angle gives evidence of aerodynamic hysteresis occurred at high angle of attack. The non-linear additional increments of the moment due to aerodynamic hysteresis are linearized by the harmonic linear method. Then, based on the harmonic balance method, an approximate analytical formula is derived for determining the characteristics of aircraft lateral-directional limit cycle oscillation induced by aerodynamic hysteresis. Calculations by this method show that the results are in good agreement with data obtained by the numerical iterating method in references[1]and[2]. The method eliminates the shortcoming in the above references that the amplitude of roll rate limit cycle oscillation induced by roll hysteresis is not the maximum.