  It is widely accepted that moduli in the mass range 10eV - $10^4$GeV which
start to oscillate with an amplitude of the order of the Planck scale either
jeopardize successful predictions of nucleosynthesis or overclose the Universe.
It is shown that the moduli problem can be relaxed by making use of parametric
resonance. A new non-perturbative decay channel for moduli oscillations is
discussed. This channel becomes effective when the oscillating field results in
a net negative mass term for the decay products. This scenario allows for the
decay of the moduli much before nucleosynthesis and, therefore, leads to a
complete solution of the cosmological moduli problem.
