A hearing device, e.g. a hearing aid, comprises a) an input unit comprising a multitude of input transducers for providing respective electric input signals representing sound in an environment of the user; b) an output unit comprising an output transducer for providing stimuli perceivable to the user as sound based on said electric input signals or a processed version thereof; c) first and second spatial filters each connected to said input unit and configured to provide respective first and second spatially filtered signals based on said multitude of electric input signals and configurable beamformer weights. The first spatial filter implements at a given time, a feedback cancelling beamformer, or a target maintaining, noise cancelling, beamformer directed at said environment of the user. The second spatial filter implements at a given time, a feedback cancelling beamformer, or an own voice beamformer directed at the mouth of the user.