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The Gibbs energy minimization using activity coefficient models and nonlinear equation solution techniques are commonly applied for phase stability problems. However, dependence on the initial estimates and multiple solutions for these highly nonlinear equations are common drawbacks for some of the conventional approaches. We have used interval Newton method with the local composition model of NRTL for the phase stability analysis of 10 binary systems and 2 ternary systems at various feed compositions to locate all the stationary points. Results indicate that the interval Newton method is reliable and efficient.