  We analyze the behaviour of moduli fields in string effective models between
the end of inflation and reheating. The effective moduli potential during this
era is derived for a class of simple models. We argue that this potential
significantly stabilizes the modulus at its high energy minimum, if some
restrictions on modular weights are met. Two mechanisms to further stabilize
the moduli to their low energy minima are discussed explicitly: coinciding
minima at a point of enhanced symmetry, and the smooth transition from high to
low energy minimum by an effective mass term C^2 H^2. For both cases we present
explicit examples, and C^2 is found to be O(10) at most. In addition, we show
that during a smooth transition the reduction of the modulus amplitude strongly
depends on the shape of the low energy potential.
