This paper reports the gas-permeation properties of poly(ethylene oxide) (PEO) poly(butylene terephthalate) (PBT) segmented multiblock copolymers. These block copolymers allow a precise structural modification by the amount of PBT and the PEO segment length, enabling a systematic study of the relationship between polymer composition and morphology and gas-transport properties. The CO2 and N2 permeability strongly varies with the amount of PEO and the PEO segment length. The permeabilities are compared to predictions of the Maxwell model, which considers the PBT phase as impermeable. The difference between the experimental values and the Maxwell model are interpreted on the basis of chain flexibility of the PEO phase. The chain flexibility decreases with increasing amounts of PBT due to a less pronounced phase separation between the PEO and PBT phase. This is reflected in an increasing glass-transition temperature of the amorphous PEO phase. The increase of the permeability with an increasing PEO block length, at the same ratio PEO-PBT, can therefore be related to a larger chain flexibility for longer PEO segments. The permeability also depends on the degree of crystallinity and the melting temperature of the PEO phase, which increases with the amount and the PEO segment length. PEO-PBT block copolymers exhibit a high CO2/N2selectivity ( 60 at T = 35 C) due to the high solubility of CO2 in the PEO phase. However, this selectivity is structure-dependent and is higher for block copolymers with larger amounts of PBT. The CO2/He selectivity shows a different structure dependency since the permeation of CO2 occurs primarily through the PEO phase and the He permeation occurs through both the PEO and mixed PEO-PBT interphase. Therefore, block copolymers with a better phase separation between the PEO phase and the PBT phase show a higher CO2/He selectivity.