A mathematical model of the flow gas-liquid continuous stirred tank reactor (CSTR) is presented under the assumption of thermodynamic equilibrium of the two-phase flow. Phase equilibrium was calculated using the Redlich-Kwong-Soave (RKS) equation of state. An efficient algorithm based on homotopy method was used to obtain a numerical solution of the system of nonlinear algebraic equations of the model. By an example of the liquid-phase hydrogenation of benzene, steady states were analyzed in isothermal and adiabatic regimes and at partial removal of heat released as a result of exothermic reaction. It was shown that under certain conditions, a multiplicity of stationary solutions is possible due to nonlinearity of the kinetic reaction, on the one hand, and deviation of the reaction mixture properties from the ideal state, on the other hand. (c) 2005 Elsevier Ltd. All rights reserved.