After the first run of LHC, no signal of new physics has been found in terms of the DM motivated
channels containing missing energy. Even though the next LHC run could still detect
a WIMP-like signal, especially from the electroweakly charged sector, we investigate in this
thesis the phenomenology of two models, beyond the SM of particle physics, for unstable DM
which are expected to show up as cosmological consistent signals at colliders. These signals
are represented by long-lived particles, metastable particles and, finally, prompt particles while
their cosmological consistency lies in the requirements that DM is in agreement with the indirect
detection constraints, the value of the present-day DM and, at last, with baryonic asymmetry
via thermal leptogenesis (only for gravitino).
