In this Letter, we show how the generic coupling of moduli to the kinetic e
nergy of ordinary matter fields results in a cosmological mechanism that in
fluences the evolution and stability of moduli. As an example, we reconside
r the problem of stabilizing the dilaton in a non-perturbative potential in
duced by gaugino condensates. A well-known difficulty is that the potential
is so steep that the dilaton field tends to overrun the correct minimum an
d to evolve to an observationally unacceptable vacuum. We show that the dil
aton coupling to the kinetic or thermal energy of matter fields produces a
natural mechanism for gently relaxing the dilaton field into the correct mi
nimum of the potential without fine-tuning of initial conditions. The same
mechanism is potentially relevant for stabilizing other moduli fields. (C)
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