We address the important issue of stabilizing the dilaton in the context of
superstring cosmology. Scalar potentials which arise out of gaugino condensates
in string models are generally exponential in nature. In a cosmological setting
this allows for the existence of quasi scaling solutions, in which the energy
density of the scalar field can, for a period, become a fixed fraction of the
background density, due to the friction of the background expansion. Eventually
the field can be trapped in the minimum of its potential as it leaves the
scaling regime. We investigate this possibility in various gaugino condensation
models and show that stable solutions for the dilaton are far more common than
one would have naively thought.Comment: 13 pages, LaTex, uses psfig.sty with 3 figure
