Stability analysis is generally faster than phase-split calculations because the Rachford-Rice equation is not part of stability testing. However, there are occasions in which one may encounter computational inefficiency and indeed divergence in the single-phase region far away from the critical point. The computational inefficiency is found in various formulations of the stability analysis calculations. In this work, the cause of the problem is explained. A simple algorithm is also presented for stability analysis calculations in the reduction method. As in the past, only the Newton method is used in the solution of nonlinear equations except in some isolated iterations when one single successive substitution (SSI) iteration may be required to avoid nonphysical conditions. Results show that the stability analysis for the proposed algorithm is fast and robust. Results also show that the simple algorithm in the reduction method is superior to the combined SSI-Newton and quasi-Newton methods with conventional variables. Results are also presented showing that the stability analysis in two-phase is faster than phase-split calculations even when the initial guess is from the stability testing. 2006 American Institute of Chemical Engineers.