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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 minimalsupersymmetric standard model (MSSM), where they are induced at the one-looplevel via box and reducible Feynman diagrams. For the numerical evaluation ofthe branching ratios we employ the decoupling limit and consider values for theMSSM parameters still consistent with the current experimental data. Weconsider a particular scenario for the radiative corrections to the Higgs bosonmasses, 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 bosondecay $A\to Z\gamma\gamma$ 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 valuesof $\tan\beta$, which is comparable with the branching ratio of the $H\toZ\gamma$ channel. As far as the branching ratio of the SM-like Higgs bosondecay $h\to Z\gamma\gamma$ is concerned, it is considerably suppressed, of theorder of $10^{-11}$.

Decay $\phi\to Z \gamma\gamma$ ($\phi=h, H,A$) in the minimal supersymmetric standard model