  The scalar and vector meson exchange contributions to the doubly radiative
decays $\eta^{(\prime)}\to\pi^0\gamma\gamma$ and
$\eta^\prime\to\eta\gamma\gamma$ are analysed within the Linear Sigma Model and
Vector Meson Dominance frameworks, respectively. Predictions for the diphoton
invariant mass spectra and the associated integrated branching ratios are given
and compared with current available experimental data. Whilst a satisfactory
description of the shape of the $\eta\to\pi^{0}\gamma\gamma$ and
$\eta^\prime\to\pi^{0}\gamma\gamma$ decay spectra is obtained, thus supporting
the validity of the approach, the corresponding branching ratios cannot be
reproduced simultaneously. A first theoretical prediction for the recently
measured $\eta^\prime\to\eta\gamma\gamma$ by the BESIII collaboration is also
presented.
