The application relates to a hearing system comprising a hearing device (HD), and a programming device (PD), and a feedback path analyzer (FPA) for providing an estimate of a feedback path from an output transducer to an input transducer of the hearing device. The hearing device (HD) and the programming device (PD) each comprises a programming interface (PI, PD-PI) allowing the exchange of data between the devices. The feedback path analyzer (FPA) is located in the programming device (PD), and the hearing device (HD) comprises respective input (IBUF) and output (OBUF) buffers for storing corresponding input and output time segments of the electric input signal or a signal derived therefrom and of the processed output signal or a signal derived therefrom, respectively. The hearing device (HD)—in a specific feedback measurement mode—is configured to transmit said stored input and output time segments of the respective signals to the feedback path analyzer (FPA) of the programming device (PD) via said programming interface (PI, PD-PI), and the feedback path analyzer (FPA) is configured to determine said estimate of the feedback path based on said (stored) input and output time segments. Thereby a more accurate estimation and/or a shorter measurement time can be achieved. The invention may e.g. be used for the fitting of hearing devices, e.g. hearing aids, to a particular use or user.