The significance of the median natural lightning currents on the energy handling capabilities of surge arresters employed in wind farms is investigated. The Electromagnetic Transient Program Alternative Transient Program (EMTP-ATP) was used to simulate direct lightning strikes to the blade of an existing wind turbine in order to determine the current discharged through the surge arresters and hence the energy absorbed by the surge arresters located at different wind turbines. The values of the energy handling capabilities of surge arresters are generally published in manufacturers' datasheets. Yet, the impact of the subsequent lightning strokes is usually ignored. Also, the published energy handling capabilities are based solely on standard waveforms. This contribution uses two sets of natural lightning current parameters measured on instrumented towers at Mount San Salvatore and Morro do Cachimbo, to simulate lightning strikes to the wind turbine blade. The results show that the influence of the subsequent strokes can be significant for the current discharged through the surge arresters and the subsequent energy absorbed, especially at the stricken turbine.