As is well known, a small compressive disturbance in an elastic gas grows into a shock wave in finite time. If the gas is viscoelastic or has internal degrees of freedom, this result is no longer true unless the initial amplitude of the disturbance is larger than acritical amplitude. This article investigates the effect of diffusion on the growth and decay properties of small disturbances in a mixture of elastic gases. It is shown that a critical amplitude exists for the mixture. Thus, diffusion can be thought of as having a stabilizing effect in that not all compressive disturbances will grow into shock waves.