Method for operating a hearing aid system for assisting a user's ability to hear, comprising at least one hearing aid instrument worn on the user's head, in particular in or on an ear, - wherein a sound signal from the user's surroundings is recorded and converted into input audio signals (I1, I2) by means of at least two input transducers of the hearing aid system, - wherein the input audio signals (I1, I2) are processed in a signal processing step to generate an output audio signal, - wherein the output audio signal is output by means of an output transducer of the hearing aid instrument, - wherein, in the signal processing step, the input audio signals (I1, I2) or audio signals (I1', I2') derived therefrom by pre-processing are direction-dependently damped by means of a first adaptive beamformer according to the stipulation of a variable first directivity with a directional strength (s) in order to generate a first directed audio signal, - wherein the first directivity is varied with a first adaptation speed in such a way during an adaptation step that the energy content of the first directed audio signal is minimized, and - wherein the first adaptation speed and/or the directional strength (s) are variably set on the basis of an analysis of the input audio signals (I1, I2) or of the pre-processed audio signals (I1', I2'), wherein for the analysis of the input audio signals (I1, I2) or of the pre-processed audio signals (I1', I2') and therefore for the purposes of setting the first adaptation speed and/or the directional strength (s), a second adaptive beamformer with a variable second directivity is applied to the input audio signals (11, I2) or the pre-processed audio signals (I1', I2') to generate a second directed audio signal, - wherein the second directivity is set with a second adaptation speed in such a way that the energy content of the second directed audio signal is minimized, - wherein the second adaptation speed does not drop below the first adaptation speed and at least intermittently exceeds the latter, and - wherein the first adaptation speed and/or the directional strength (s) are set depending on a deviation of the second directivity from the first directivity, namely depending on the deviation of a second notch direction assigned to the second directivity from a first notch direction assigned to the first directivity, wherein the first adaptation speed is increased and/or the directional strength (s) is reduced if and for as long as the deviation of the second notch direction from the first notch direction exceeds a specified threshold. - wherein a sound signal from the user's surroundings is recorded and converted into input audio signals (I1, I2) by means of at least two input transducers of the hearing aid system, - wherein the input audio signals (I1, I2) are processed in a signal processing step to generate an output audio signal, - wherein the output audio signal is output by means of an output transducer of the hearing aid instrument, - wherein, in the signal processing step, the input audio signals (I1, I2) or audio signals (I1', I2') derived therefrom by pre-processing are direction-dependently damped by means of a first adaptive beamformer according to the stipulation of a variable first directivity with a directional strength (s) in order to generate a first directed audio signal, - wherein the first directivity is varied with a first adaptation speed in such a way during an adaptation step that the energy content of the first directed audio signal is minimized, and - wherein the first adaptation speed and/or the directional strength (s) are variably set on the basis of an analysis of the input audio signals (I1, I2) or of the pre-processed audio signals (I1', I2'), wherein for the analysis of the input audio signals (I1, I2) or of the pre-processed audio signals (I1', I2') and therefore for the purposes of setting the first adaptation speed and/or the directional strength (s), a second adaptive beamformer with a variable second directivity is applied to the input audio signals (11, I2) or the pre-processed audio signals (I1', I2') to generate a second directed audio signal, - wherein the second directivity is set with a second adaptation speed in such a way that the energy content of the second directed audio signal is minimized, - wherein the second adaptation speed does not drop below the first adaptation speed and at least intermittently exceeds the latter, and - wherein the first adaptation speed and/or the directional strength (s) are set depending on a deviation of the second directivity from the first directivity, namely depending on the deviation of a second notch direction assigned to the second directivity from a first notch direction assigned to the first directivity, wherein the first adaptation speed is increased and/or the directional strength (s) is reduced if and for as long as the deviation of the second notch direction from the first notch direction exceeds a specified threshold.