A disagreement between effective sizes of elementary free volumes found from the four component PAT-FIT analyses of positronium annihilation lifetime spectra and experiments on low temperature sorption for two membrane materials of internal microporosity poly(tri-methyl-silyl-propyne) PTMSP and spirolinked benzodioxane polymer PIM-1 is described and discussed. This disagreement can be minimized essentially using the fifth lifetime component but not the Gaussian distribution of the fourth component. 1 Introduction Elastic and glassy polymers are normally considered as homogeneous disordered materials with a unimodal (statistical) distribution of elementary free volumes. More complex (bicentral) distributions, obtained from mathematical analyses of experimental positron annihilation lifetime spectra (PALS), were explained recently as "artefacts", i.e. results of incorrect mathematical treatment (de-convolution) of the spectra. Accepting this conclusion as a reasonable formal explanation in some cases, we discussed [1] results of our PAL measurements for a number of elastic and glassy polymers, such as polystyrene (normal and cross-linked) poly-isobutylene poly-butadiene, synthetic rubbers, etc., where observations of the two long-lived ortho-positronium components in PALS, comparison with the results of sorption experiments and irregular (nonlinear) variations of annihilation characteristics in the vicinity of the glass-transition temperature actually revealed structural heterogeneity, confirmed by supplementary techniques: measurements of thermo-stimulated luminescence (TSL), thermo-mechanics, and mobility of penetrants in the systems. The heterogeneity was explained by slow relaxation of the polymer structures. Continuing this line of investigations, we present in this paper annihilation characteristics and sorption data for two membrane materials of internal microporosity: well known poly(tri-methylsilyl-propine) PTMSP [2-4] and a novel material spiro-linked benzodioxane polymer PIM-1 [5,6].A combination of PAL experiments and sorption data for membrane materials is very important for understanding of the mechanisms of Ps annihilation and potential applications of the positron annihilation research. This combination enables testing of the PAL data on the large (1-2nm) pores. Along with