  Neutralinos arise as natural dark matter candidates in many supersymmetric
extensions of the Standard Model. We present a novel calculation of the
neutralino relic abundance in which we include all so called coannihilation
processes between neutralinos, charginos and sfermions, and, at the same time,
we apply the state of the art technique to trace the freeze-out of a species in
the early Universe. As a first application, we discuss here results valid in
the mSUGRA framework; we enlight general trends as well as perform a detailed
study of the neutralino relic densities in the mSUGRA parameter space. The
emerging picture is fair agreement with previous analyses in the same
framework, however we have the power to discuss it in many more details than
previously done. E.g., we find that the cosmological bound on the neutralino
mass is pushed up to ~565 GeV in the stau coannihilation region and to ~1500
GeV in the chargino coannihilation region.
