  The contribution of axial-vector mesons to the muon's anomalous magnetic
moment through a light-by-light process is considered within a nonlocal quark
model. The model is based on a four-quark interaction with scalar--pseudoscalar
and vector--axial-vector sectors. While the transverse component of the
axial-vector corresponds to a spin-1 particle, the unphysical longitudinal
component is mixed with a pseudoscalar meson. The model parameters are
re-fitted to the pion properties in the presence of pi-a_1 mixing. The obtained
estimation for the light-by-light contribution of a_1+f_1 mesons is
(3.6+-1.8)*10^{-11}.
