We analyze the behaviour of moduli fields in string effective models b
etween the end of inflation and reheating. The effective moduli potent
ial during this era is derived for a class of simple models. We argue
that this potential significantly stabilizes the modulus at its high e
nergy minimum, if some restrictions on modular weights are met. Two me
chanisms to further stabilize the moduli to their low energy minima ar
e discussed explicitly: coinciding minima at a point of enhanced symme
try, and the smooth transition from high to low energy minimum by an e
ffective mass term (CH2)-H-2. For both cases we present explicit examp
les, and C-2 is found to be O(10) at most. In addition, we show that d
uring a smooth transition the reduction of the modulus amplitude stron
gly depends on the shape of the low energy potential.