Positron annihilation lifetime (PAL) spectroscopy was applied to measure free-volume size distribution in polymer samples with unusually long lifetimes : in dense films of poly(trimethylsilylpropyne) (PTMSP) and in porous membranes prepared from poly(phenylene oxide) (PPO). PAL data were treated by finite-term lifetime analysis (PATFIT program) and continuous lifetime analysis (CONTIN program). Lifetime distributions of positron annihilation in these samples consist of two positronium components : in the range 1-2 and 4-8 ns (PTMSP) and in the range 20-70 ns (porous PPO). In the case of PTMSP the longer lifetimes correspond to continuous free-volume size distribution in the range R = 4.5-5.5 Angstrom. These radii are much larger than those characteristic for "normal" glassy polymers. A good agreement was obtained between the parameters of PAL distributions obtained by means of PATFIT and CONTIN programs in PTMSP and PPO dense films. An analysis of the CONTIN peak widths of free-volume size distribution in different polymers both studied in this work and reported in the literature indicated that the ratio of peak width and average radius R-av levels off at larger sizes of free volume. An estimate of the diffusion coefficient of positronium was made for PPO samples with different surface area.