We study the nonperturbative structure of the axial current and evaluate the two-point light-cone distribution amplitudes (DA) associated with the correlator integral d xi e(-iq.xi) < 0 vertical bar(psi) over bar (x) Gamma psi(y) J(mu)(5) (xi)vertical bar 0 > within the instanton vacuum model in the leading order in O(N-c). Due to the built-in chiral symmetry, four of eight axial DAs are related to that for pions. Knowledge of these nonperturbative objects is important for phenomenological study of high-energy neutrino interactions and semileptonic decays of heavy quarks. We provide a code for evaluation of these DAs and an interpolation formula valid in the region Q(2) less than or similar to 1 GeV2. (C) 2013 Elsevier B.V. All rights reserved.