The LbL contribution to the muon g-2 from the axial-vector mesons exchanges within the nonlocal quark model

The light-by-light contribution from the axial-vector (AV) mesons exchanges to the muon anomalous magnetic moment is estimated in the framework of the nonlocal chiral quark model. The preliminary answer for contributions from a1 and f1 mesons to (g-2)_mu is 0.34 x 10^(-11) and does not support the Melnikov-Vainshtein estimate 2.2 x 10^(-11).