  At the end of inflation, the inflaton field decays into an initially
nonthermal population of relativistic particles which eventually thermalize. We
consider the production of dark matter from this relativistic plasma, focusing
on the prethermal phase. We find that for a production cross section
$\sigma(E)\sim E^n$ with $n> 2$, the present dark matter abundance is produced
during the prethermal phase of its progenitors. For $n\le 2$, entropy
production during reheating makes the nonthermal contribution to the present
dark matter abundance subdominant compared to that produced thermally. As
specific examples, we verify that the nonthermal contribution is irrelevant for
gravitino production in low scale supersymmetric models ($n=0$) and is dominant
for gravitino production in high scale supersymmetry models ($n=6$).
