  To elucidate the composition of dark matter (DM) is one of the most important
open questions in particle and astroparticle phenomenology. Within the
framework of minimal supersymmetric extensions of the standard model of
fundamental particles, the `mu-from-nu supersymmetric standard model',
$\mu\nu$SSM, solves the $\mu$-problem and reproduces neutrino data, only adding
couplings involving right-handed neutrinos. In this context, the supersymmetric
partner of the graviton, known as gravitino, becomes a natural DM candidate.
Working in the mentioned model, in this thesis we have analyzed the detection
of gamma-ray signals arising from decaying gravitino DM considering experiments
such as $\textit{Fermi}$-LAT. For this purpose all gravitino decays have been
taken into account, complementing previous works. The possibility of an
upcoming new generation of gamma-ray detectors has motivated the inclusion of
axino, the supersymmetric partner of the axion, as a DM candidate. In this
thesis, axino DM has been analyzed in the context of the $\mu\nu$SSM for the
first time. Finally, scenarios with multicomponent DM have been studied,
focusing on gravitinos and axinos coexisting as DM constituents. This novel
scenario includes two very different cases with distinctive features: axino
lighter than gravitino and vice versa. Considering the sensitivity of future
MeV-GeV gamma-ray telescopes, axino and gravitino prospects of detection were
analyzed in the mixed scenarios mentioned previously. In some parameter space
regions, both candidates can produce a signal, therefore a double-line feature
arises as a smoking gun that would uncover the DM composition.
