  We consider the minimal supersymmetric extension of the Standard Model
allowing both Dirac and Majorana gauginos. The Dirac masses are obtained by
pairing up extra chiral multiplets: a singlet S for U(1)_Y, a triplet T for
SU(2) and an octet O for SU(3) with the respective gauginos. The electroweak
symmetry breaking sector is modified by the couplings of the new fields S and T
to the Higgs doublets. We discuss two limits: i) both the adjoint scalars are
decoupled with the main effect being the modification of the Higgs quartic
coupling; ii) the singlet remaining light, and due to its direct coupling to
sfermions, providing a new contribution to the soft masses and inducing new
decay/production channels. We discuss the LSP in this scenario; after
mentioning the possibility that it may be a Dirac gravitino, we focus on the
case where it is identified with the lightest neutralino, and exhibit
particular values of the parameter space where the relic density is in
agreement with WMAP data. This is illustrated for different scenarios where the
LSP is either a bino (in which case it can be a Dirac fermion) or
bino-higgsino/wino mixtures. We also point out in each case the peculiarity of
the model with respect to dark matter detection experiments.
