The transport rates of methanol and water through a series of PEBAX(R) block copolymers were measured and correlated with the fractional free volume. Excellent agreement between the logarithm of the diffusion coefficient and the inverse of the fractional free volume of the polymer was observed. This provides new evidence of the utility of the free volume theory to describe the transport of highly condensable vapours. Correlation was also quite good when the logarithmic additivity relationship was employed. This relationship has been previously shown to correlate the properties of homogenous blends with copolymer composition. The successful use of this theory for a series of blends that exhibit two glass transition temperatures is discussed.