  We consider here the dynamics of some homogeneous and isotropic cosmological
models with $N$ interacting classical scalar fields non-minimally coupled to
the spacetime curvature, as an attempt to generalize some recent results
obtained for one and two scalar fields. We show that a Lyapunov function can be
constructed under certain conditions for a large class of models, suggesting
that chaotic behavior is ruled out for them. Typical solutions tend generically
to the empty de Sitter (or Minkowski) fixed points, and the previous asymptotic
results obtained for the one field model remain valid. In particular, we
confirm that, for large times and a vanishing cosmological constant, even in
the presence of the extra scalar fields, the universe tends to an infinite
diluted matter dominated era.
