  Typically the moduli fields acquire mass m =C H in the early universe, which
shifts the position of the minimum of their effective potential and leads to an
excessively large energy density of the oscillating moduli fields at the later
stages of the evolution of the universe. This constitutes the cosmological
moduli problem, or Polonyi field problem. We show that the cosmological moduli
problem can be solved or at least significantly relaxed in the theories in
which C >> 1, as well as in some models with C << 1.
