  The cosmological relic density of a Bino-like Lightest Supersymmetric
Particle is calculated in the framework of the Minimal Supersymmetric Standard
Model. We include annihilation and coannihilation effects of the Bino with the
lightest stau and with the other sleptons, which happen to have comparable
masses with it. Coannihilation turns out to be crucial for reducing the Bino
relic density to an acceptable level. Phenomenological constraints, also,
results from the inclusion of the supersymmetric corrections to the CP-even
Higgs boson and b-quark masses and the branching ratio of b -->s gamma. We
impose these constraints on two versions of the Minimal Supersymmetric Standard
Model, employing radiative electroweak breaking with universal boundary
conditions and gauge coupling unification. In the first version of the model we
assume Yukawa coupling unification and boundary conditions from
gravity-mediated supersymmetry breaking. In the second version of the model we
assume boundary conditions from the Horava-Witten theory and we restrict the
parameter space by simultaneously imposing the phenomenological and
cosmological constraints.
