Positron annihilation lifetime spectroscopy (PALS) is applied to a series of bis(aniline)fluorene and bis(xylicline)fluorene-based cardo polyimide and bis(phenol)fluorene-based polysulfone membranes. It was found that favorable amounts of positronium (Ps, the positron-electron bound state) form in cardo polyimides with the 2,2-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydride (6FDA) moiety and bis(phenol)fluorene-based cardo polysulfone, but no Ps forms in most of the polyimides with pyromellitic dianhydride (PMDA) and 3,3',4,4'-biphenyltetracarboxylic dianhydride (BTDA) moieties. A bis(xylidine)fluorene-based polyimide membrane containing PMDA and BTDA moieties exhibits a little Ps formation but the ortho-positronium (o-Ps, the triplet state of Ps) lifetime of this membrane anomalously shortens with increasing temperature, which we attribute to chemical reaction of o-Ps. Correlation between the hole size (V-h) deduced from the o-Ps lifetime and diffusion coefficients of O-2 and N-2 for polyimides with the 6FDA moiety and cardo polysulfone showing favorable Ps formation is discussed based on free volume theory of gas diffusion. It is suggested that o-Ps has a strong tendency to probe larger holes in rigid chain polymers with wide hole size distributions such as those containing cardo moieties, resulting in deviations from the previously reported correlations for common polymers such as polystyrene, polycarbonate, polysulfone, and so forth.