  Motivated by recent BABAR measurements of the $\gamma^*\to\gamma \eta$ and
$\gamma^*\to\gamma \eta^\prime $ transition form factors, we estimate
two-photon exchange contributions to the corresponding cross sections. By using
a phenomenological model, based on the vector meson dominance, it is argued
that the expected contributions are small enough not to effect the BABAR
results. As a by product we predict $Br(\eta^\prime\to\mu^+\mu^-)= (1.4\pm
0.2)\times 10^{-7}$. Our results might be useful also in high precision
calculations of radiative corrections to the Dalitz decays of pseudoscalar
mesons.
