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AbstractIn this paper we consider flat and open universe models 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 we consider the perturbed universe as a dynamical system, described by coupled differential equations for a gauge- invariant perturbation variable and a relevant background variable. The phase-space analysis of this dynamical system shows that flat dust-radiation models are unstable, and open models structurally unstable, with respect to adiabatic perturbations. For flat models, there are actually three different regimes of evolution for the perturbations, depending on their wavelength and the transition scale from one regime to the other is determined by a critical wavenumber for the perturbations, kEC (an invariant of the model). We find that kEC &lt; kJE (the Jeans wavenumber at equidensity of matter and radiation), implying that there are perturbations which decay even if their wavelength at equidensity is larger than the corresponding Jeans scale. We also briefly discuss metric and curvature perturbations. 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.