Two non-ideal, multiphase chemical reaction equilibrium algorithms are presented. An approach to multiphase equilibrium calculations due to Abdel-Ghani et al. [R.M. Abdel-Ghani, EOS mixing rules for multi-phase behaviour, MS thesis, University of Calgary, Calgary, 1995; R.M. Abdel-Ghani, R.A. Heidemann, A.V. Phoenix, Paper presented at the 1994 AIChE Conference, San Francisco, CA, 1994] was modified to include reaction equilibrium, exploiting two proposals by Michelsen [M.L. Michelsen, Fluid Phase Equilibria 53 (1989) 73-80; M.L. Michelsen, Computers Chem. Eng. 18 (1994) 545-550]. In both algorithms, nested processes are used with an inner loop treating the phases as ideal solutions and an outer loop updating non-ideal parts of the models. Both of the algorithms were initiated with a number of phases which were reduced in the outer loop by combining phases as they approach the same composition and density. Initiation strategies for phase amounts and compositions are presented. (C) 1998 Elsevier Science B.V. All rights reserved.