  The epochs of reheating and preheating are studied in a simple extension of
the Starobinsky inflationary model, which consists of an $R^2$--correction to
the Einstein--Hilbert action and an additional scalar field. We find that if
the $R^2$--correction at the end of inflation is dynamically important, it
affects the expansion rate and as a consequence the reheating and preheating
processes. While we find that the reheating temperature and duration of
reheating are only slightly affected, the effect has to be taken into account
when comparing the theory to data. In the case of preheating, the gravitational
corrections can significantly affect the decay of the second field. Particle
production is strongly affected for certain values of the parameters in the
theory.
