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 describe general trends as well as performing 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 much more detail than previously done. For example, we find that the cosmological bound on the neutralino mass is pushed up to similar to 565 GeV in the stau coannihilation region and to similar to 1500 GeV in the chargino coannihilation region.
