  We study reheating in some one and two field realizations of {\it Fibre
Inflation}. We find that reheating begins with a phase of preheating in which
long wavelength fluctuation modes are excited. In two field models there is a
danger that the parametric amplification of infrared fluctuations in the second
scalar field - associated with an entropy mode - might induce an instability of
the curvature fluctuations. We show that, at least in the models we consider,
the entropy mode has a sufficiently large mass to prevent this instability.
Hence, from the point of view of reheating the models we consider are
well-behaved.
