Electrolyte systems constitute an important class of chemical and phase equilibrium mixtures. They usually involve complex speciation in the aqueous solution and formation of solid phases. For geochemical systems in particular, the number of species, solids and speciation reactions is often large. In this study, we extend the application of two recently developed non-stoichiometric methods to multiphase chemical equilibrium in electrolyte systems: the first-order Lagrange multipliers method and the second-order modified RAND method. The methods are based on the Gibbs energy minimization approach with Lagrange multipliers as elemental chemical potentials and they are suitable to systems with many reactions and many phases. We demonstrate that the overall electroneutrality condition is always satisfied as long as the material balance is met. Therefore, the two methods can be directly applied to electrolyte systems while special caution is needed for the different reference states used in the electrolyte models. In addition, the stability analysis for pure solid formation can be expressed in a compact form using the Lagrange multipliers. We present three examples with emphasis on geochemical reactions. The aqueous phase can be at equilibrium with a vapor phase consisting of the volatile components and multiple solid phases. Formation of vapor and solid phases does not impede convergence or affect the convergence rate. For the geochemical system with three solid phases, our methods are orders of magnitude faster than PHREEQC. (C) 2018 Published by Elsevier B.V.