  We generalize the dispersive approach to axial anomaly by A.D. Dolgov and
V.I. Zakharov to a non-Abelian case with arbitrary photon virtualites. We
derive the anomaly sum rule for the singlet current and obtain the
$\pi^0,\eta,\eta'\rightarrow\gamma\gamma^*$ transition form factors. Using
them, we established the behavior of a nonperturbative gluon matrix element
$\langle 0 |G\tilde{G} |\gamma\gamma^*(q^2) \rangle$ in both spacelike and
timelike regions. We found a significant contribution of the non-Abelian axial
anomaly to the processes with one virtual photon, comparable to that of the
electromagnetic anomaly. The duality between the axial and the vector channels
was observed: the values of duality intervals and mixing parameters in the
axial channel were related to vector resonances' masses and residues. The
possibility of a light pseudoscalar glueball-like state is conjectured.
