  Using a sample of $(225.3\pm 2.8)\times 10^{6}$ $J/\psi$ decays collected
with the BESIII detector at BEPCII, searches for invisible decays of $\eta$ and
$\eta^\prime$ in $J/\psi\to\phi\eta$ and $\phi\eta^\prime$ are performed.
Decays of $\phi \to K^{+}K^{-}$ are used to tag the $\eta$ and $\eta^\prime$
decays. No signals above background are found for the invisible decays, and
upper limits at the 90% confidence level are determined to be
$2.58\times10^{-4}$ for the ratio
$\frac{\mathcal{B}(\eta\to\rm{invisible})}{\mathcal{B}(\eta\to\gamma\gamma)}$
and $2.39\times10^{-2}$ for
$\frac{\mathcal{B}(\eta^\prime\to\rm{invisible})}{\mathcal{B}(\eta^\prime
\to\gamma\gamma)}$.
