Buffeting forces of structures such as transmission tower usually have highly nonlinear relation to incoming wind fluctuations. Based on wind forces and simultaneous fluctuating wind speed measured from wind tunnel test on a model of 1000kV suspension transmission tower, aerodynamic coefficients and aerodynamic admittance functions are studied. Unsteady aerodynamic coefficients obtained in the test are compared with those estimated starting from linear and Gaussian assumptions. The concept of total aerodynamic admittance including structural aerodynamic damping effect is suggested, which is identified by ratio of power spectral density of wind force to that of fluctuating wind speed. The linear admittances, which represent correlated parts of the wind speeds and wind forces, are also calculated by employing frequency-domain coherence functions. Results show that linear assumption of relationship between time-dependent wind angle of attack and associated aerodynamic coefficient lends more accuracy than Gaussian assumption. Because of the unsteady nature of wind-speed-to-wind-force relation, neglect of aerodynamic admittances will lead to conservative estimation of buffeting responses of the structure. Moreover, effects of wind fluctuations will be underrated if linear admittances are adopted in spite of the prominent nonlinearity between wind speed and wind force.