Abstract Meson-exchange corrections of the nuclear axial current are derived and expanded up to relativistic order ( 1 m N ) 2 . They are obtained from a phenomenological chiral-invariant lagrangian based on the exchange of π-, ϱ- and A 1-mesons. The axial exchange currents are appropriate for general calculations of weak nuclear properties. The paper tests them for the Gamow-Teller matrix element of tritium β-decay. The theoretical prediction of the Gamow-Teller matrix element is, within the theoretical uncertainty, in fair agreement with its experimental value.