  We provide the complete set of radiative corrections to the Dalitz decays
$\eta^{(\prime)}\to \ell^+\ell^-\gamma$ beyond the soft-photon approximation,
i.e. over the whole range of the Dalitz plot and with no restrictions on the
energy of a radiative photon. The corrections inevitably depend on the
$\eta^{(\prime)}\to\gamma^*\gamma^{(*)}$ transition form factors. For the
singly virtual transition form factor appearing e.g. in the bremsstrahlung
correction, recent dispersive calculations are used. For the
one-photon-irreducible contribution at the one-loop level (for the doubly
virtual form factor), we use a vector-meson-dominance-inspired model while
taking into account the $\eta$-$\eta^\prime$ mixing.
