  The branching ratio of the electromagnetic rare decays
$\eta\to\pi^0\gamma\gamma$ and $\eta^\prime\to (\pi^0,\eta)\gamma\gamma$ are
analysed in terms of scalar and vector meson exchange contributions using the
frameworks of the Linear Sigma Model and Vector Meson Dominance, respectively.
The measured $\eta\to\pi^0\gamma\gamma$ process serves as a test of our
approach while the non yet measured $\eta^\prime\to (\pi^0,\eta)\gamma\gamma$
reactions are predicted for the first time. Our prediction for the
$\eta\to\pi^0\gamma\gamma$ decay agrees with recent experimental reported
values, thus supporting the validity of our framework. Therefore, our
predictions for the $\eta^\prime\to\pi^0\gamma\gamma$ and
$\eta^\prime\to\eta\gamma\gamma$ decays should be taken as a first indication
of the possible values of the associated branching ratios. We hope these
predictions to be interesting and useful for experiments such as KLOE-2,
Crystal Ball, WASA, and BES-III where these processes are expected to be
measured in the next future.
