Joulia, X., Maggiochi, P., Koehret, B., Paradowski, H. and Bartuel, J.J., 1986. Hybrid method for phase equilibrium flash calculations. Fluid Phase Equilibria, 26: 15–36. A new algorithm for the calculation of a two-phase equilibrium at a given temperature and pressure using various thermodynamic models is described. This algorithm is a combination of two simultaneous solution methods based on a linearization of the system of equations with or without the partial derivatives of equilibrium ratios with respect to composition. This hybrid method exploits the reliability of the first order methods, which make good progress from a poor starting point, and, if necessary, switches on special application of the Schubert method to accelerate the rate of convergence. Results are reported for liquid—liquid and liquid—vapour equilibria with special attention in the vicinity of critical points.