Patton, C.L., Green, K.A. and Luks, K.D., 1992. Analysis of the N-Component N-Phase Equilibrium Extremum Problem. Fluid Phase Equilibria, 72: 267-275. the General Condition for a Pressure Extremum in the N-Component N-Phase Composition Surface When Projected Onto Pressure-Temperature Coordinates is Identified. for N = 2, the Physical Situation is Well Known, Being Either the State of Criticality (Liquid = Gas) or Azeotropy (X1g = X11). for N > 2, It is Shown that the Extremum Results from the Existence of a Linear Relation between the Compositions of the N Phases, with Azeotropy Being a Special Case of that Constraint. © 1992.