The general condition for a pressure extremum in the n-component n-pha
se composition surface when projected onto pressure-temperature coordi
nates 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 exi
stence of a linear relation between the compositions of the n phases,
with azeotropy being a special case of that constraint.