  The impact of a kination-dominated phase generated by a quintessential
exponential model on the thermal abundance of gravitinos and axinos is
investigated. We find that their abundances become proportional to the
transition temperature from the kination to the radiation era; since this
temperature is significantly lower than the initial ("reheating") temperature,
the abundances decrease with respect to their values in the standard cosmology.
For values of the quintessential energy-density parameter close to its upper
bound, at the eve of nucleosynthesis, we find the following: (i) for unstable
gravitinos, the gravitino constraint is totally evaded; (ii) If the gravitino
is stable, its thermal abundance is not sufficient to account for the cold dark
matter of the universe; (iii) the thermal abundance of axinos can satisfy the
cold dark matter constraint for values of the initial temperature well above
those required in the standard cosmology. A novel calculation of the axino
production rate by scatterings at low temperature is also presented.
