A hearing aid system assists a user's ability to hear. The system has a hearing aid instrument worn on the user's head. A sound signal from the user's surroundings is recorded and converted into input audio signals by two input transducers. The input audio signals are processed in a signal processing step for generating an output audio signal, which is output by an output transducer. The input audio signals or audio signals derived therefrom by pre-processing are direction-dependently damped by an adaptive beamformer according to the stipulation of a variable directivity with a directional strength to generate a directed audio signal. The directivity is varied with a specified adaptation speed such that the energy content of the directed audio signal is minimized. The adaptation speed and/or the directional strength are variably set on a basis of an analysis of the input audio signals or of the pre-processed audio signals.