A hearing aid adapted for being worn by a user at or in an ear of the user comprises a) at least one input transducer for converting sound in an environment around the user to at least one electric input signal representing said sound; b) an output transducer for converting a processed output signal provided in dependence of said at least one electric input signal to stimuli perceivable to the user as sound; c) a feedback control system comprising an adaptive filer, the feedback control system being configured to provide an adaptively determined estimate (h*(n)) of a current feedback path (h(n)) from said output transducer to said at least one input transducer in dependence of c1) said at least one electric input signal, c2) said processed output signal, and c3) an adaptive algorithm. The hearing aid further comprises d) a database comprising a multitude (M) of previously determined candidate feedback paths (hm); and e) a controller configured to identify a change in the current feedback path (h(n)) based on the adaptively determined estimate (h*(n)) of the current feedback path and at least one of said multitude of previously determined candidate feedback paths (hm). A method of operating a hearing aid is further disclosed. The invention may e.g. be used in hearing aids, e.g. binaural hearing aid systems or headsets, or speakerphones, or combinations thereof.