A simple free volume model for permeability (P) and diffusivity (D) of polymers has been used to obtain various linear correlations of the type log P-i versus logP(j) or log D-i versus logD(j) for gas pairs M-i and M-j. These correlations are proven for several hundred glassy polymers and various gas pairs. An important implication of this result is that it predicts the well-known tradeoff relation between permeability P-i and permselectivity P-i/P-j considered by many authors. Possible ways for improving the combination of these two parameters of membrane polymeric materials are discussed. In particular, the role of sorption selectivity and its enthalpic and entropic contributions are emphasized.