The gas transport properties of polymer nanocomposite membranes made of Few Layer Graphene nanoplatelets dispersed in amine-modified epoxy resins were studied by gas phase permeation analysis with H-2, N-2 and CO2. The gas permeability of the nanocomposites decreases with increasing filler content. Filler addition does not change the gas selectivity of the pure epoxy membrane. Positron Annihilation Lifetime Spectroscopy analysis indicates that, by increasing the filler content, the free volume structure does not change but the fractional free volume decreases. Gas transport results were explained by the formation of a constrained polymer region of thickness l(if) at the filler-matrix interface. The l(if) parameter was evaluated from the reduction of the fractional free volume of the nanocomposite samples with respect to that of the epoxy matrix. The average value of l(if), similar to 20 nm, permits to reproduce quantitatively the experimental data at all examined temperatures, filler concentration and test gas. (C) 2017 Elsevier Ltd. All rights reserved.