  Flat and open universe models are considered, containing a mixture of cold
matter (dust) and radiation interacting only through gravity, with the aim of
studying their stability with respect to linear scalar perturbations. To this
end the perturbed universe is considered as a dynamical system, described by
coupled differential equations for a gauge\hs invariant perturbation variable
and a relevant background variable. The phase\hs space analysis of this
dynamical system shows that flat dust\hs radiation models are unstable, and
open models structurally unstable, with respect to adiabatic perturbations. It
is shown that there are perturbations which decay even if their wavelength at
equidensity is larger than the corresponding Jeans scale. Metric and curvature
perturbations are also briefly discussed. We believe that this analysis gives a
clearer idea of the stability properties of realistic universe models than the
standard one based on the Jeans scale, despite our simplifying assumptions.
