A hearing device with a plurality of microphones is intended to be able to be continued to be operated sensibly, even if a microphone fails. Therefore, a hearing device, and in particular a hearing aid, is proposed which provides a decision unit for deciding whether one of the microphones is defective, and a signal processing unit for processing the signals from the microphones using a plurality of processing algorithms. The signal processing unit switches from a first one of the processing algorithms to a second one of the processing algorithms if a decision is made in the decision unit that one of the microphones is defective. In particular, if a microphone fails, automatic switching from directional microphone operation into omnidirectional operation is for example made possible.