Gas permeability coefficients for several gases (He, CO2, CH4, O2 and N2) were measured at 25-degrees-C in a series of semicrystalline diblock copolymers of polyethylene/poly(ethylene-propylene). A simple model is presented describing the gas transport in these polymer systems. It predicts the permeability of a randomly oriented spherulitic diblock specimen from the values of the permeability coefficients of the individual lamellar regions of the copolymer. Model predictions were in excellent agreement with the experimental data. The upper bound (lamellae aligned in parallel with respect to the permeation direction) and lower bound (series lamellar alignment) models were calculated and compared to a limited amount of corresponding experimental data on oriented specimens.