  Many models of supersymmetry breaking, in the context of either supergravity
or superstring theories, predict the presence of particles with
Planck-suppressed couplings and masses around the weak scale. These particles
are generically called moduli. The excessive production of moduli in the early
Universe jeopardizes the successful predictions of nucleosynthesis. In this
paper we show that the efficient generation of these dangerous relics is an
unescapable consequence of a wide variety of inflationary models which have a
preheating stage. Moduli are generated as coherent states in a novel way which
differs from the usual production mechanism during parametric resonance. The
corresponding limits on the reheating temperature are often very tight and more
severe than the bound of 10^9 GeV coming from the production of moduli via
thermal scatterings during reheating.
