Gas separation membranes allow the preferential removal of certain gases from a mixture of gases. If the separation objective is to obtain high product purity and either high removal efficiency or high product recovery it is often necessary to implement a multi-stage network of membranes. However, in the literature most modelling approaches consider the simulation of single-stage membranes. Hence, the aim of this study is to identify stable and computationally efficient strategies for simulating complex multi-stage membrane systems. For this purpose a multi-stage membrane modelling framework is developed and six different stable solution strategies are evaluated and compared in terms of the computational effort required to solve the resulting sets of equations. These solution strategies vary according to the sequence in which the individual membrane models are solved (sequential and simultaneous approaches) and the manner in which those membrane models are initialised. In all these strategies a Newton-Raphson method is employed to solve the mass balance equations in both single-stage and multi-stage membrane systems. Comparisons are made using example simulations of 10 different configurations of membranes containing 1-4 membranes with different numbers of connections and recycle streams present. (C) 2015 Elsevier B.V. All rights reserved.