  Anomalous triangle graphs for the divergence of the axial-vector current are
studied using the dispersive approach generalized for the case of higher orders
of perturbation theory. The validity of this procedure is proved up to two-loop
level. By direct calculation in the framework of dispersive approach we have
obtained that the two-loop AVV amplitude is equal to zero. According to the
Vainshtein's theorem the transversal part of the anomalous triangle is not
renormalized in the chiral limit. We generalize this theorem for tha case of
finite fermion mass in the triangle loop.
