Mathematical models have been developed for an internally two-staged hollow fibre permeator for the cases of co/counter-current and counter/co-current flow patterns. A comparative study on the performance of these two flow patterns together with two other flow patterns, i.e. cocurrent flow and countercurrent flow, has been conducted using gas mixtures of O-2/N-2 and CO2/N-2. It has been shown, both theoretically and experimentally, that in terms of achieving a higher permeate enrichment, the co/counter-current mode is always the most efficient one followed by cocurrent flow, while the counter/co-current and countercurrent flow patterns are less efficient. The experimental results are generally in good agreement with theoretical predictions.