A model that describes the critical flow of chemically reacting, two-phase, multicomponent mixtures in channels of constant cross section is discussed. As a consequence of an assumed interphase thermal and mechanical equilibrium the applicability of the model is restricted to situations where one phase is intimately mixed with the other, such that choking is determined by the sound speed in the homogeneous mixture. It is shown that under certain conditions the highly non-linear temperature dependency of the reaction rate promotes the possibility of a multiplicity of steady state solutions to the problem.