Interfacial stability in crystal growth by dissociative sublimation has been investigated quantitatively, by use of a simple model, as a function of parameters over which crystal growers have control. It is found that there is a critical value of the growth rate, Jcrit, for the interface to be stable, which varies dramatically with the composition of the gas phase, and with small values of the temperature gradient near the growing surface. Two further important aspects are shown clearly by the treatment : (1) The temperature difference ΔTcrit between the source and the growing surface, corresponding to the critical growth rate Jcrit, becomes small if (a) the ratio αl of components in the gas phase near the source is close to that in the solid, or (b) the temperature gradient near the growing surface is small (–1). Moreover, the growth rate varies rapidly for temperature differences ΔTΔTcrit, and is therefore sensitive to small temperature fluctuations. (2) If αl is very different from the stoicheiometric ratio in the solid, the growth rate J is insensitive to ΔT for J near Jcrit. However, in this case, the ratio α0 of components in the gas phase near the growing surface becomes a sensitive function of ΔT, so that the composition of the grown solid becomes sensitive to small temperature fluctuations. The treatment is general; however, a familiar case (cadmium sulphide) is included as an illustration.