Multiple solutions may arise in membrane separators when the mole fraction of a component with intermediate permeability is specified as a design variable. Two necessary conditions for the presence of two solutions are shown in this paper. One of these conditions can be simplified if the pressure in the permeate chamber is significantly lower than that of the rententate. The simplified necessary conditions are equations that involve only the composition of the feed and the permeabilities of the membrane. A sufficient condition arises whenever both necessary conditions are satisfied.