  The results on chaos in FRW cosmology with a massive scalar field are
extended to another scalar field potential. It is shown that for sufficiently
steep potentials the chaos disappears. A simple and rather accurate analytical
criterion for the chaos to disappear is given. On the contrary, for gently
sloping potentials the transition to a strong chaotic regime can occur. Two
examples, concerning asymptotically flat and Damour-Mukhanov potentials are
given.
