  Preheating following the inflationary phase in models of open inflation is
considered. The most significant difference from a preheating scenario in flat
space is that supercurvature modes can be populated and amplified in the open
universe. In certain models, such modes can dominate the usual resonant
particle production, thus altering the ensuing thermal history within an open
universe. The accuracy to which the masses and couplings need to be tuned to
produce such supercurvature modes, however, makes any large deviation from the
flat space cases unlikely.
