A hearing device, e.g. a hearing aid, comprises a) at least one input transducer for converting sound in the environment of the hearing device to respective at least one acoustically received electric input signal or signals representing said sound; b) a wireless receiver for receiving an audio signal from a wireless transmitter of a sound capturing device for picking up sound in said environment and providing a wirelessly received electric input signal representing said sound; and c) a processor configured c1) to receive said at least one acoustically received electric input signal or signals, or a processed version thereof; c2) to receive said wirelessly received electric input signal; and c3) to provide a processed signal. The processor comprises a signal predictor for estimating future values of said wirelessly received electric input signal in dependence of a multitude of past values of said signal, thereby providing a predicted signal. The hearing device further comprises d) an output transducer for presenting output stimuli perceivable as sound to the user in dependence of said processed signal from said processor, or a further processed version thereof. The processor is configured to provide said processed signal in dependence of the predicted signal or a processed version thereof 1) alone, or 2) mixed with said at least one acoustically received electric input signal or signals, or a processed version thereof. A hearing device comprising an earpiece and a separate audio processing device is further disclosed. The invention may e.g. be used in hearing devices in wireless communication with audio capture devices in an immediate environment of the user wearing the hearing device.