  In many cases a nonlinear scalar field with potential $V$ can lead to
accelerated expansion in cosmological models. This paper contains mathematical
results on this subject for homogeneous spacetimes. It is shown that, under the
assumption that $V$ has a strictly positive minimum, Wald's theorem on
spacetimes with positive cosmological constant can be generalized to a wide
class of potentials. In some cases detailed information on late-time
asymptotics is obtained. Results on the behaviour in the past time direction
are also presented.
