  We study the cosmological evolution of the volume moduli in a class of
recently proposed Inflationary Universe models arising out of Type IIB string
theory, where a number of the moduli fields have been stabilised through flux
compactifications. Developing an approach initially introduced in [3] we show,
in agreement with [4], how the presence of extra sources of matter act so as to
provide additional friction, slowing the modulus field as it evolves down its
potential, thereby vastly increasing the region of parameter space which leads
to the eventual stabilisation of these fields. Extending the case to include
both the real and imaginary parts of the volume modulus, we show how the
parameter space of inital conditions is modified and comment on the impact for
these inflationary models arising out of flux type compactifications.
