  The decays of the CP-even ($h,\,H$) and the CP-odd ($A$) Higgs bosons
$h,\,H,\,A\to Z\gamma\gamma$ are calculated in the context of the minimal
supersymmetric standard model (MSSM), where they are induced at the one-loop
level via box and reducible Feynman diagrams. For the numerical evaluation of
the branching ratios we employ the decoupling limit and consider values for the
MSSM parameters still consistent with the current experimental data. We
consider a particular scenario for the radiative corrections to the Higgs boson
masses, dubbed hMSSM, which leads to only two free parameters, namely $m_A$ and
$\tan\beta$. We found that the branching ratio of the $CP$-odd Higgs boson
decay $A\to Z\gamma\gamma$ can reach values up to $10^{-8}$ for $m_A=750$ GeV,
which is three order of magnitude smaller than that of the $A\to\gamma\gamma$
channel. On the other hand, the branching ratio of the $H\to Z\gamma\gamma$
decay is of the order of $10^{-7}$ for large values of $m_H$ and small values
of $\tan\beta$, which is comparable with the branching ratio of the $H\to
Z\gamma$ channel. As far as the branching ratio of the SM-like Higgs boson
decay $h\to Z\gamma\gamma$ is concerned, it is considerably suppressed, of the
order of $10^{-11}$.
