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We examine the main properties of relic neutralinos in the context of the Minimal Supersymmetric extension of the Standard Model. We present a whole set of results obtained for the relic abundance and for detection rates with a model constrained according to the latest accelerator data. Predicted detection rates for relic neutralinos are compared to the present experimental bounds. A comparison with results obtained with more sophisticated theoretical schemes with unification assumptions at M_{GUT} is presented too. We also briefly discuss some properties of a Higgsino-like neutralino which has recently been suggested in connection with a supersymmetric interpretation of a single event at the Fermilab Tevatron.

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