Input multiplicity is an important feature of industrial processes. In this paper, we extend the work by Tiscareno et al. [1998. Multiplicity of the solutions of the flash equations. Chemical Engineering Science 53, 671-677] to analyze multiple solutions of the flash equations when a product mole fraction of one component is specified and the vapor fraction or the temperature is calculated. For this type of multiplicity to arise, at least one stationary point for the mole fractions with respect to vapor fraction or temperature must exist. By using a constant relative volatility model, we demonstrate the uniqueness of the stationary point, and show the necessary and sufficient conditions for the existence of such a stationary point. From these results one can state that systems with a constant relative volatility assumption can only present second-order input-multiplicities. (c) 2006 Elsevier Ltd. All rights reserved.