  The most recent results from direct searches for dark matter particles in the
galactic halo are examined in terms of an effective Minimal Supersymmetric
extension of the Standard Model at the electroweak scale without gaugino masses
unification. We show that the annual modulation effect at 8.2 $\sigma$ C.L.
recently presented by the DAMA Collaboration, as the result of a combined
analysis of the DAMA/NaI and the DAMA/LIBRA experiments for a total exposure of
0.82 ton yr, fits remarkably well with what expected for relic neutralinos for
a wide variety of WIMP distribution functions. Bounds derivable from other
measurements of direct searches for dark matter particles are analyzed. We
stress the role played by the uncertainties affecting the neutralino--quark
couplings arising from the involved hadronic quantities. We also examine how
present data on cosmic antiprotons can help in constraining the neutralino
configurations selected by the DAMA effect, in connection with the values of
the astrophysical parameters.
  Perspectives for measurement of antideuterons possibly produced in the
galactic halo by self--annihilation of neutralinos belonging to the DAMA
configurations are examined. Finally, we discuss how findings at LHC would
impact on these issues.
