Model-based optimisation is demonstrated for the design and analysis of two generalised membrane systems: a single stage permeator in which then is the recycle of both retentate and permeate gases, and a continuous membrane column in which there is the additional recycle of the retentate stream to the feed line. Multitubular shell-and-tube arrangements are considered with the counter-current flow of tube and shell-side gases; attention is given to the separation of air over several commercial polymeric membranes. A finite element technique is used for the solution of the model equations, and optimisation achieved through standard successive reduced quadratic programming methods. In specific, the maximisation of the Rony separation index is considered at various user-specified product oxygen purities. On this basis, a membrane column is shown to out-perform a single-stage permeator. Optimisation of the Rony index also leads to favourable composition profiles in the enricher and stripper sections of the membrane column, in which, for example, reverse permeation is avoided, and the extent of mixing (dilution) of feed minimised. Furthermore, the optimisation strategy is found to be approximately analogous to the maximisation of the equivalent pure oxygen and nitrogen production rates. Optimisation results for the membrane column indicate the benefits of a relatively small degree of retentate reflux, but negligible benefit of any retentate recycle to the feed line. For a given membrane column size and feed processing rate, membranes of low selectivity (but high permeability) are also shown to yield more favourable molar splits of oxygen and nitrogen than membranes of high selectivity, but at the expense of compressor power requirements. Issues of membrane column scale-up and intensification are also addressed by application of scaling ratio theory to the optimal designs. The theory indicates that for a membrane column designed for the maximum molar split of oxygen and nitrogen, a reduction in compressor power, whilst maintaining this split, can only be achieved at the: expense of reduced feed throughput.