  The recently observed ultra-high energy (UHE) cosmic rays beyond the
Greisen-Zatsepin-Kuzmin bound can be explained by the decays of some superheavy
$X$ particles forming a part of dark matter in our universe. We consider
various discrete gauge symmetries ${\bf Z}_N$ to ensure the required long
lifetime ($\tau_X \simeq 10^{10}-10^{22} years$) of the $X$ particle to explain
the UHE cosmic rays in the minimal supersymmetric standard model (MSSM) with
massive Majorana neutrinos. We show that there is no anomaly-free discrete
gauge symmetry to make the lifetime of the $X$ particle sufficiently long in
the MSSM with the $X$ particle. We find, however, possible solutions to this
problem especially by enlarging the particle contents in the MSSM. We show a
number of solutions introducing an extra pair of singlets $Y$ and $\bar{Y}$
which have fractional ${\bf Z}_N$ (N=2,3) charges. The present experimental
constraints on the $X$ particle are briefly discussed.
