  It is shown that spatially homogeneous solutions of the Einstein equations
coupled to a nonlinear scalar field and other matter exhibit accelerated
expansion at late times for a wide variety of potentials $V$. These potentials
are strictly positive but tend to zero at infinity. They satisfy restrictions
on $V'/V$ and $V''/V'$ related to the slow-roll approximation. These results
generalize Wald's theorem for spacetimes with positive cosmological constant to
those with accelerated expansion driven by potentials belonging to a large
class.
