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The most recent results from direct searches for dark matter particles in thegalactic halo are examined in terms of an effective Minimal Supersymmetricextension of the Standard Model at the electroweak scale without gaugino massesunification. We show that the annual modulation effect at 8.2 $\sigma$ C.L.recently presented by the DAMA Collaboration, as the result of a combinedanalysis of the DAMA/NaI and the DAMA/LIBRA experiments for a total exposure of0.82 ton yr, fits remarkably well with what expected for relic neutralinos fora wide variety of WIMP distribution functions. Bounds derivable from othermeasurements of direct searches for dark matter particles are analyzed. Westress the role played by the uncertainties affecting the neutralino--quarkcouplings arising from the involved hadronic quantities. We also examine howpresent data on cosmic antiprotons can help in constraining the neutralinoconfigurations selected by the DAMA effect, in connection with the values ofthe astrophysical parameters.  Perspectives for measurement of antideuterons possibly produced in thegalactic halo by self--annihilation of neutralinos belonging to the DAMAconfigurations are examined. Finally, we discuss how findings at LHC wouldimpact on these issues.

Interpreting the recent results on direct search for dark matter particles in terms of relic neutralino