  We have studied the lightest masses in the fermionic sector of an anomalous
$U(1)'$ extension of the Minimal Supersymmetric Standard Model (MSSM) inspired
by brane constructions. The LSP of this model is an XWIMP (extremely weak
interaction particle). We have studied its relic density in the cases in which
there is mixing with the neutralinos of the MSSM and in the case in which there
is not such mixing. We have showed that this extended model can satisfy the
WMAP data. To perform this calculation we have modified the DarkSUSY package.
