  The asymptotic behaviour of two classes of scalar field cosmological models
are studied using the theory of dynamical systems: general relativistic Bianchi
models containing matter and a scalar field with an exponential potential and a
class of spatially homogeneous string cosmological models. The purpose of this
thesis is to examine some of the outstanding problems which currently exist in
cosmology, particularly regarding isotropization and inflation. It is shown
that the matter scaling solutions are unstable to curvature perturbations. It
is then shown that the Bianchi class B exponential potential models can
alleviate the isotropy problem; an open set of models within this class do
isotropize to the future. It is also shown that the presence of an interaction
term in the subclass of isotropic models can lead to inflationary models with
late-time oscillatory behaviour in which the matter is not driven to zero.
Next, within the class of the string cosmologies studied, it is shown that
there is a subclass which do not inflate at late times in the post-big bang
regime. Furthermore, all string models studied typically do not have a
late--time flatness problem. Indeed, it is shown that curvature typically plays
an important r\^{o}le only at intermediate times in most models. It is also
shown that the presence of a positive cosmological constant in the models
studied can lead to interesting physical behaviour, such as multi-bouncing
universes. A mathematical equivalence between general relativistic scalar field
theories and scalar-tensor theories and string theories has been extensively
exploited and thus the results obtained from the string analysis compliment the
results obtained from the Bianchi class B exponential potential analysis.
