  The relic density of a cold dark matter (CDM) candidate is calculated in the
context of three non-standard cosmological scenaria and its value is compared
with the one obtained in the standard regime. In particular, we consider the
decoupling of the CDM particle during: (i) A decaying-particle dominated phase
or (ii) a kinetic-energy dominated phase or (iii) the decay of a massive
particle under the complete or partial domination of kination. We use plausible
values (from the viewpoint of supersymmetric models) for the mass and the
thermal averaged cross section times the velocity of the cold relic and we
investigate scenaria of equilibrium and non-equilibrium production. In the case
(i) a low reheat temperature, in the range (1-20) GeV, significantly
facilitates the achievement of an acceptable CDM abundance. On the other hand,
the presence of kination in the case (ii) can lead to an enhancement of the CDM
abundance up to three orders of magnitude. The latter enhancement can be
avoided, in the case (iii). In a such situation, the temperature turns out to
be frozen to a plateau value which is, mostly, lower than about 40 GeV.
