Valid solutions to the multicomponent equilibrium problem are commonly but not invariably unique roots of the governing equations. Modelers for this reason need to consider the possibility of the existence of more than one mathematically correct root to the equations describing chemical equilibrium in multicomponent systems. This chapter demonstrates the origin of nonunique roots to the equilibrium problem, provides several worked examples of how such roots may arise, and gives advice about coping with the possibility of nonuniqueness.