Kuhn-Tucker optimization theory is employed to obtain new results for the problem of the determination of equilibria in multi-phase multi-reaction systems. The results provide a complete classification of the possible types of behaviour that can occur for such systems. In this classification, there is an essential difference between the cases of systems for which no reactions have a set of stoichiometric coefficients that sum algebraically to zero, and systems for which this is not the case. The results yield a geometric interpretation that can be viewed as an extension of the corresponding interpretation of the geometry of systems undergoing phase equilibria alone. Illustrations are given of all possible cases of binary and ternary reacting systems.