A stability analysis of the ordinary differential equations describing the process of convective gas-phase-controlled evaporation during drying is performed. Isothermal and non-isothermal as well as batch and continuous drying processes are considered. For isothermal evaporation of a ternary mixture into pure gas, the solutions of the differential equations are trajectories in the phase plane represented by a triangular diagram of compositions. The predicted ternary dynamic azeotropic points are unstable or saddle. On the other hand, binary azeotropes are stable when the combination of the selectivities of the corresponding components is negative. In addition, pure component singular points are stable when they are contained within their respective isolated negative selectivity zones. Under non-isothermal conditions, stable azeotropes are characterized by presenting maximum temperature values. Loading the gas with one or more of the components up to some value leads to a node-saddle bifurcation, where a saddle azeotrope and a stable azeotrope coalesce and disappear. The continuous drying process yields similar results for both flat and annular geometries. The singular points, in this case, are infinite and represent dynamic equilibrium points whose stability is mainly dependent on the inlet gas-to-liquid flowrate ratio. As this ratio grows to infinity, the phase portrait changes and the process approaches a batch behaviour so that the stability analysis for that case may be applied. The present stability analysis permits the prediction of trajectories and final state of a system in a gas-phase-controlled drying process.