  We update the theoretical framework for the QCD calculation of transition
form factors $\gamma^*\gamma\to\eta$ and $\gamma^*\gamma\to\eta'$ at large
photon virtualities including full next-to-leading order analysis of
perturbative corrections, the charm quark contribution, and taking into account
SU(3)-flavor breaking effects and the axial anomaly contributions to the
power-suppressed twist-four distribution amplitudes. The numerical analysis of
the existing experimental data is performed with these improvements.
