  We consider the phenomenological implications of gravitino dark matter in the
context of the $\mu\nu$SSM. The latter is an R-parity breaking model which
provides a solution to the $\mu$-problem of the MSSM and explains the origin of
neutrino masses by simply using right-handed neutrino superfields. In
particular, we analyze the prospects for detecting gamma rays from decaying
gravitinos. Gravitino masses larger than 20 GeV are disfavored by the isotropic
diffuse photon background measurements, but a gravitino with a mass range
between $0.1 - 20$ GeV gives rise to a signal that might easily be observed by
the FERMI satellite. Through this kind of analysis important regions of the
parameter space of the $\mu\nu$SSM can be checked.
