  In this paper we study the dynamical behaviour of a simple cosmological model
defined by a spatially flat Robertson-Walker geometry, conformally coupled with
a massive scalar field. We determine a Lyapunov-like function for the
non-linear evolution equations. From this function we prove that all the
stationary solutions are unstable. We also show that all initial conditions,
different from the stationary points, originate an expanding universe in the
asymptotic regime, with a scale parameter $a(t)$ that goes to infinity and the
scalar field $\phi (t)$ that goes to zero in an oscillatory way . We also find
two asymptotic solutions, valid for sufficiently large values of time. These
solutions correspond to a radiation dominated phase and to a matter dominated
phase, respectively.
