Epoxy membranes with same chemical structure but different free volumes were prepared using aliphatic epoxide and polyether diamines as cross-linking agents. Their fractional free volume f h (T) was previously evaluated as a function of temperature and cross-linking density [PN Patil et al., PhysChemChemPhys 18 (2016) 3817–3824]. Original H 2 permeation measurements were performed changing sample temperature and network structure and compared with CO 2 and N 2 transport data. Modelling gas permeability Φ in the framework of the free volume theory we observe that the Arrhenius-type behavior of Φ for test gases is consequence of the f h (T) linear increase with temperature and that at equal f h value membranes exhibit increasing Φ values by decreasing the cross-linking density. Analysis of permeability data on this set of test molecules with different size and condensation properties suggests that increasing the cross-linking between polymer chains limits their thermal fluctuations and the redistribution of the free volume elements where diffusional jumps of penetrant molecules occur.