  We study the late time evolution of flat and negatively curved FRW models
with a perfect fluid matter source and a scalar field having an arbitrary
non-negative potential function $V(\phi) .$ We prove using a dynamical systems
approach four general results for a large class of non-negative potentials
which show that almost always the universe ever expands. In particular, for
potentials having a local zero minimum, flat and negatively curved FRW models
are ever expanding and the energy density asymptotically approaches zero. We
investigate the conditions under which the scalar field asymptotically
approaches the minimum of the potential. We discuss the question of whether a
closed FRW with ordinary matter can avoid recollapse due to the presence of a
scalar field with a non-negative potential.
