A binaural hearing assistance system comprising first and second hearing assistance devices (HAD l, HAD r) adapted for being located at or in or fully or partially implanted in the head at left and right ears of a user, wherein each of the first and second hearing assistance devices (HAD l, HAD r) comprises a) a first wireless interface comprising first inductor and transceiver circuitry (Tx1, Rx1) adapted for establishing a first communication link (1 st -WL) to the respective other hearing assistance device based on near-field communication; b) a second wireless interface comprising second antenna and transceiver circuitry (Tx2, Rx2) adapted for establishing a second communication link (2 nd -WL) to an auxiliary device based on far-field communication; c) an energy source; d) an energy source status monitoring circuit configured to monitor a current status of the energy source and provide an energy status indication signal (ESlnd), and to exchange said energy status indication signal (ESlnd) with the other hearing assistance device of the binaural hearing assistance system via the first and/or the second communication link (1 st -WL, 2 nd -WL); e) a link control unit operatively coupled to the energy source status monitoring circuit, and the link control unit is further operatively coupled to the first inductor and/or the second antenna and transceiver circuitry, and wherein in each hearing assistance device, the energy status indication signal (ESlnd) generated in and received from the opposite hearing assistance device is fed to the link control unit for comparison with the locally generated energy status indication signal (ESInd); wherein f) the link control unit is configured to repeatedly provide a second link quality measure indication of a link quality of the second communication link (2 nd -WL, 2 nd -WL), and wherein the first and second hearing assistance devices (HAD l, HAD r) are configured to exchange the second link quality measures between them via the first and/or second communication links (1 st -WL, 2 nd -WL); and g) wherein the link control unit is configured to provide a predetermined priority or priority algorithm for weighting the influence of the second link quality measure and the energy status indication signal (ESlnd) in the control of the first and/or second communication links (1 st -WL, 2 nd -WL). a) a first wireless interface comprising first inductor and transceiver circuitry (Tx1, Rx1) adapted for establishing a first communication link (1 st -WL) to the respective other hearing assistance device based on near-field communication; b) a second wireless interface comprising second antenna and transceiver circuitry (Tx2, Rx2) adapted for establishing a second communication link (2 nd -WL) to an auxiliary device based on far-field communication; c) an energy source; d) an energy source status monitoring circuit configured to monitor a current status of the energy source and provide an energy status indication signal (ESlnd), and to exchange said energy status indication signal (ESlnd) with the other hearing assistance device of the binaural hearing assistance system via the first and/or the second communication link (1 st -WL, 2 nd -WL); e) a link control unit operatively coupled to the energy source status monitoring circuit, and the link control unit is further operatively coupled to the first inductor and/or the second antenna and transceiver circuitry, and wherein in each hearing assistance device, the energy status indication signal (ESlnd) generated in and received from the opposite hearing assistance device is fed to the link control unit for comparison with the locally generated energy status indication signal (ESInd); wherein f) the link control unit is configured to repeatedly provide a second link quality measure indication of a link quality of the second communication link (2 nd -WL, 2 nd -WL), and wherein the first and second hearing assistance devices (HAD l, HAD r) are configured to exchange the second link quality measures between them via the first and/or second communication links (1 st -WL, 2 nd -WL); and g) wherein the link control unit is configured to provide a predetermined priority or priority algorithm for weighting the influence of the second link quality measure and