The dispersive approach to axial anomaly was generalized 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. The relevant low energy theorem was generalized to the case of mixed states and used to evaluate the subtraction constant of the strong anomaly-related form factor $\langle 0 |G\tilde{G} |\gamma\gamma \rangle$. Using expressions for transition form factors, we established the behaviour of a non-perturbative gluon matrix element $\langle 0 |G\tilde{G} |\gamma\gamma^*(q^2) \rangle$ in both space-like and time-like 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. From the analysis of the experimental data we established existence of a non-zero $\pi^0-\eta-\eta'$ mixing. The possibility of a light pseudoscalar glueball-like state is conjectured.

Decays of scalar mesons $K^*_0(800) \to K\pi$ and $K^*_0(1430) \to K\pi, K \eta, K \eta', K_1 \pi$ are described in the extended $U(3) \times U(3)$ Nambu--Jona-Lasinio chiral quark model. The obtained results are in satisfactory agreement with the new experimental data obtained by the BaBar collaboration, which markedly differ from the existing values in the PDG.