In nonideal chemical systems in which chemical reactions occur in more than one phase, more than one equilibrium condition may be calculated, but only one of them will be stable. In this research, a nonlinear optimization is applied to locale all minima of the Gibbs free energy function, from which the global stable solution can be ascertained. To find multiple solutions to the chemical and phase equilibria (CPE) problems in nonideal systems homotopy continuation is applied, accounting for bifurcation phenomena. Solution branches are traced by pseudo-arclength continuation.