A method for operating a wind energy installation having a tower, a nacelle arranged on the tower, the azimuth of which can be adjusted, and a rotor having at least one rotor blade, the blade angle of which can be adjusted, in which tower oscillations are detected and monitored during operation using at least one measuring apparatus and power operation is switched off if a sliding average of the tower oscillations exceeds a tower oscillation limit value. The tower oscillation limit value is defined, at least during load operation of the wind energy installation, as at least one limit value function which is dependent on a sliding average of prevailing wind speed and/or a parameter associated therewith, and has different functional dependencies in a plurality of different value ranges of the prevailing wind speed or the parameter associated therewith. The invention also relates to a wind energy installation.